I am a fucking loser

It's a joke that's made a lot, how Batman is supposed to be a loner, and yet he has one of the most extensive Families and ally circles in DC. But once you get to know the character, it's not at all a contradiction. Bruce lost his family, and that trauma shaped him. It's the basis of Batman. It makes perfect sense that he'd yearn to create one of his own... but the problem is, his desire for connection is many times outweighed by his absolute, paralyzing fear of it. If he has a family, if he has people he cares about, then he can lose them. Bruce is terrified of loss, and this fear is one of the main roots of his pattern of emotional abuse.

This pattern tends to manifest in three forms. The first is neglect. He distances himself from his children, treats them as soldiers in his neverending war on crime, keeps them at arms length -- both because he wants it to hurt less if he loses them, and because he's never developed a healthy way of dealing with his own or others' emotions. In many ways, it's self-preservation, and not just towards the Family. In general, Bruce's repression, intellectualization, and emotional distancing is a way to avoid being hurt. This drives his belief that emotional attachments are, in the end, a weakness. He can't focus on the Mission if he's constantly worried about the people fighting alongside him... but he also needs them. And here one of Bruce's darker traits come in, too: his ruthlessness. He can't be everywhere all at once, he can't operate alone and be as efficient as when having a small army of trained soldiers at his side. For the sake of the Mission being fulfilled, and with the goal of protecting Gotham and saving as many people as possible, he allows the Batfamily to exist. Bruce is capable of 'turning off' his emotions and only acting in the interest of a higher goal, in a way that's hurt and pissed off his friends and Family multiple times. I'm not at all saying he doesn't love them, or care about them. That's the crux of the matter. He does care, and he's afraid of what happens when he cares, which again and again prompts him to act cold and distant and emotionally push them away. But, ironically enough, it's this exact same issue that leads him to display the third kind of emotionally abusive behavior: excessive control.

Bruce has been shown to be invasive and manipulative, wanting the Family to follow his orders and punishing them in various ways when they don’t -- because, if you're terrified of losing something, one way to ensure you're not going to lose it is to contain it, and never take your eyes off it. Carefully control it. See, he can't entirely cut all ties, both because he loves the Family and because he needs them from a utilitarian point of view. But he can try to emotionally protect himself by distancing, and he can try to protect them by controlling them... by knowing everything that goes on in their lives, and (sadly) trying to get them to make choices he would make. He’s got a bit of a thing when it comes to rewarding the Family for acting the same way he does. It’s a complicated mix of Bruce’s arrogance, God complex and that controlling overprotective streak I mentioned; it’s ‘I think of every worst-case scenario and prepare for everything and train for everything and essentially try to become God, so if you act the same way I do, you will be safer and less likely to get hurt.’

The third form of his emotionally abusive pattern is the expectation for others to prioritize and handle his emotions. This pretty much follows the other two kinds; Bruce does say very hurtful things, he pushes people away, he keeps secrets and refuses to ask for help or include his children in intimate aspects of his life; but he also expects them to not let him do it, and it's... this one is really tough. I don't think it's ever quite hit him, the realization of his egocentrism: the way he makes so many things about himself. His emotions and his state of being are the priority, for his kids, and they always watch out for Bruce's anger, for his self-destructive tendencies, for signs of him retreating so they can pull him back from the brink, and the thing is, that's not their job. The kid is not supposed to take care of the parent, it's supposed to be the other way around. But more often than not, it's not Bruce handling his childrens' emotions, it's them navigating his. Dick and Tim, especially, are subject to this. Hell, Tim basically became Robin because he saw how Bruce was spiralling and went 'is no one gonna take care of that??', stepping into the role himself when Dick refused to (and good for him). And thing is, while a huge part of why Bruce adopted and trained them is empathizing with their traumas and caring about them, another part of it is... a need for grounding himself. Bruce knows he's always walking the line. He knows he's got a lot of darkness that he's always fighting to keep contained, and he can't manage it alone. He keeps himself human through his connections, his attachments; his Family, most of all. And so, it's not surprising that his children end up having to chase Bruce and figure out his emotions and take care of him, make him socialize and act like a person -- it's part of why Bruce forged these relationships in the first place. But it's still not fair to any of them. And it's impacted them in various unhealthy ways. There's certainly an argument to be made that some of them began to base their value, and self-worth, in how useful they were to Bruce. Bruce's approval is something that's so deeply craved in the core Family circle, and it's... sigh. It's downright insidious, sometimes. Bruce does so many shitty things, but they keep coming back, often at token signs of apology from Bruce or barely any crumbs at all.

And if it were only that. But Bruce's grief and his fear of loss always turn to anger. Batman is fueled by that anger, and Bruce has... lots of issues in dealing with it and venting it in a healthy way (see the above general issues in handling his own emotions). And so, you have the pattern of physical abuse, and not just the emotional I described above. In his grief and his anger, Bruce has exploded and hit his children more than once. It's tough to say who suffered more from this: Dick or Jason. Maybe Jason, since Bruce's tremendous amount of guilt and self-hatred towards him just turns into more anger, and that translates into even more potential violence. Especially when Jason breaches Bruce's rules. He gets very angry when anyone breaches his imposed rules, especially the no-killing one, and here’s where his harmful need for absolute control and some of that arrogance come in. Bruce justifies this kind of behavior in various ways (and the narrative does too, because it has to -- Batman has to be the hero), the most prevalent excuse being his treatment of them as soldiers, or a downright refusal to admit he’s even viewed as a father figure by them. This is an overarching issue in itself, his reluctance to admit he’s wrong.

In the end, so much of this has roots in Bruce’s trauma, which is the main reason why I don’t see it as OOC. He tries to save everyone because he couldn’t save his parents back then. He’s so controlling because he cannot even conceive of ever being that helpless again; he’s terrified of losing the people he cares about and still so incandescently angry at the criminals that took them away. Needless to say, he’s plenty neurodivergent, too. And disappearing for over a decade and training for being Batman, being away from Alfred and having his parents taken away at such a young age... never afforded him the opportunity to learn healthy ways of emotionally regulating himself. Neither did it teach him to reach out to others in a healthy way. And all the resulting issues, that he’s never truly dealt with constructively, converge in all the ways Bruce has fallen into abusive behaviors as a parental figure.

There are multiple moments in which Bruce has allowed for death to happen. For example, Batman #420 has him famously let KGBeast die (this is retconned later by Bruce telling Dick he did call the Police, but Dick still calls him out on it being an afterthought -- his first intention had been to let KGBeast die). Batman #613 has Bruce accidentally push two thugs into a meat grinder, something he's clearly very distraught about; but it's not something that stops him from being Batman. Batman: Run, Riddler, Run has him believe he killed someone on accident, and... he doesn't seem terribly peeved about it, though it does shake him a little. Final Crisis #6 has him shoot Darkseid with a gun intending to kill (and you know what, All-Star Batman and Robin doesn't exist, what do you mean??). Hell, Bruce allows for the possibility of Joker's death alone on three separate occasions: in Death in the Family when he lets Joker crash with the helicopter, in No Man's Land when he steps aside and allows Gordon to shoot him, and at the end of Joker War when he walks away while Joker is strapped to a bomb. Granted, all these times Bruce either thought Joker would survive, trusted Gordon was too good to shoot, and was sure Joker had the tools to disarm the bomb -- but it's still a risk, Joker could have died. Arguably, in Batman: Endgame Bruce even kills himself and Joker directly! He stops Joker from healing and keeps him with him until the caves collapse on their heads.

Even more telling, in Batman: Gotham Knights #74, Bruce actually leaves Hush behind with Joker, knowing full well he might get killed; this is pretty much all spelled out. And obviously, Joker doesn't lose respect for Batman, or have his obsession diminish afterwards. Not after this, not after the times Bruce didn't save him, not even after the time Bruce technically, genuinelly killed him.

Bruce's no-killing rule is... very complicated. Enough that books on ethics and morality have been written about it. But at its core, it's not about morality, it's about emotion. Bruce came up with it as a result of trauma, not as a result of philosophizing and ethical debate. Intentionally and selfishly killing a criminal is the line he draws in the sand, to keep his darkness at bay. Which is why the times he's come close to it are times he can justify: if it was accidental, if it was the only choice to save the Universe, if he didn't commit the act himself (like with Hush, or KGBeast, or Joker).

But if he snaps someone's neck himself, kills someone for no other reason than his own need for it (fear and anger, which for Bruce are pretty much interchangeable), that goes against the Vow. That ends Batman, because it turns Batman into Someone Like Him, the man who killed his parents; and we basically have proof of this with the premise of Batman Beyond. Bruce doesn't even genuinely kill someone in that Universe, but the fact he took a gun in his hand and considered doing it out of fear, selfishly... it destroys Batman. More importantly though, we have proof of this with The War of Jokes and Riddles, and the time he nearly stabbed Riddler out of anger, but Joker stopped him. Joker knew letting him do it like this would undo Batman, and he needed Batman to keep existing. That's why Bruce tells Selina later, "What separates me from them... is a hand on a knife. His hand."

So, knowing all this, to finally answer your question... Joker knows that Batman has allowed for his rule to bend. He's been there for a lot of those times (I didn't even mention Batman: Hush, the time Jim Gordon had to be the hand on the knife, the person to stop Bruce from going over the edge). But clearly, it hasn't affected Joker's love, or his obsession -- because he shares the belief that these times don't count. But what he does think counts, is The Batman Who Laughs (TBWL).

TBWL perfectly embodies a Bruce who's properly gone dark. He does not kill accidentally or for the greater good. He razes worlds to the ground out of fear, anger, a desire to win; he represents Batman's need for control brought to paroxysm. He's a Batman who's crossed the line. And Joker canonically, genuinely hates him. He calls TBWL an abomination, and he teams up with Bruce to take him down in Dark Nights: Metal #6. Moreso, in Snyder's Elseworld Batman ending, The Last Knight on Earth, Joker does not consider the Bruce who's become Omega and a ruthless killer a Batman anymore. So... if Bruce intentionally killed someone else, out of anger and hatred, I do think Joker would feel betrayed. He wouldn't be able to recognize him anymore, and would likely try to kill Bruce for real (in some grand murder-suicide kind of gesture). If Batman stops being Batman, in whatever capacity, Joker's life loses meaning. But more than that, I think part of trying to kill this Bruce who’s lost himself would be the love. Joker would be trying to put Batman out of his misery, stop him from being the thing he hates most. After all, in The Batman Who Laughs comic, Bruce himself asks Joker to kill him if he became that monster. And Joker very readily agrees, and is the one to shoot Bruce in the end, snapping him out of it. Keeping Bruce from going over the edge.

Joker, the hand on the knife. It’s all so... [incoherent garbled noises].

As we all know, Bruce has a sacred pattern. If someone is in direct danger of dying, he saves them. It does not matter who it is, criminal or innocent. It's an emotional compulsion rather than an ethical choice: when Bruce saves someone, he's saving his parents, in all the ways he was too weak to as a child. However, life is never that simple. When Bruce has to save criminals he despises, he expresses how much he hates that he does it; except that his need to save life, to overwrite the trauma of his childhood, is bigger than the hatred he holds for all evildoers. (Though not always. As I mentioned in my previous answer going over Bruce's no-killing rule, certain circumstances can stifle his need to save just enough for him to leave someone in mortal danger -- but there have to be enough degrees of separation so he can justify it.)

So, him saving Joker's life, no matter the circumstances, is genuinely driven by his no-killing rule and his core compulsion to save people. It's not just an excuse. Joker knows this... Hell, everyone knows this. It's something many villains take advantage of in their fights with Batman. Make him choose between chasing the perpetrator and saving an innocent life, and bam; he saves the innocent life, you get the time to escape.

But is Joker just part of the pattern? Is it just unfortunate that Joker's life needed to be saved so many times? Aaaaand... here's where the funny (tragic?) part comes in, because obviously, the answer is no. It's one thing that Bruce refuses to let anyone die, it's one thing that he's saved Joker more times and more passionately than anyone else -- but the thing is, he's saved Joker to the detriment of innocents. And this is where his no-killing rule becomes an excuse, as you call it, rather than the truth.

The Joker: Devil's Advocate has Joker condemned to death by law, but because it's for the one crime he didn't commit, Bruce goes nuts trying to save Joker's life.

It's a flimsy excuse, because Bruce breaks laws left and right, by his own admission; it's always about justice, not the rules. And yet now the law matters? Bruce very well knows Joker is guilty. He might not have committed this crime, but he's done all the others before it, and he deserves to die for those ten times over. Why not let justice follow its course, when so many innocent lives would be saved by having Joker gone (not to mention how many avenged)? You can't even argue it's about Bruce's compulsion to save lives, because I don't remember him trying to save every single criminal put on death row.

Interestingly enough, Bruce then justifies it differently towards Alfred and Tim:

Huh. You mean that you can't let Joker take the fall for this crime first, and then use the evidence you collect because you 'loathe mysteries' so much (a valiant effort on Alfred's part to justify Bruce's behavior, tbh) after, to bring the real killer in? It's not even like he'd have to wait long...

So, Bruce can't let Joker die for a crime he didn't commit because it's against the law. Then, he can't let Joker die because it allows for the real criminal to go free, and that would kill innocents. But also, his detective mind just craves solving the case so badly, and that's the reason he's doing this.

First excuse was dismantled by Gordon himself. Second excuse still does not explain why he's so urgently trying to solve the case, before Joker's death day comes around. Third excuse explains it even less, because he can just solve the case, sate his curiosity, save the innocent lives and stop the criminal-- and not hand in the evidence to save Joker's life. Just hand it in a minute later!

And here we have the fourth excuse, which actually goes against what he told Gordon. Bruce tells Joker himself that it's about justice. All different reasons, and some of them contradicting each other! But finally, the narrative directly calls him out on simply caring, where before we get comments from other characters ("I have never seen him look so... grim," says Tim. "He hasn't slept in days," says Tim.)

It truly is quite funny to me how all of Bruce's justifications don't manage to explain how desperate he is to beat the clock, don't manage to cover up the fact he's solving the case to save Joker's life; not to protect innocents, not to abide the law, not to sate his detective instincts. And if there's still any shred of doubt that Bruce is doing this for utterly selfish reasons, this is what Bruce does after he manages to get Joker pardoned literally seconds before he gets fried in the electric chair:

The comic is full of Joker's victims advocating for him dying! Full of people asserting how Joker deserves to die, because of the people he's killed, and because of how many people will die if he keeps living. And yet, after all of that, Bruce goes to Joker's cell to brag to him that he owes his life to Batman. Unhinged! Unhinged, your honor! You can't really explain Bruce in this comic in a way that makes sense without admitting that Bruce is personally invested in Joker, and that's that.

Which leads me to the most bonkers example of him choosing Joker over someone else... Batman: Under the Red Hood.

(Fucking hell, Bruce. At least go to Jason and try to help stop the bleeding.)

Just for comparison's sake. Here's Bruce stepping away and allowing for Jim Gordon to potentially kill Joker after he murdered Sarah Essen-Gordon, but then Jim shoots him in the leg (Detective Comics #741):

What is the difference between these two instances? Why didn't Bruce let Jason shoot Joker -- arguably, someone much closer to him, someone who's like a son to him, someone who Joker killed?

It's because Jason would've shot Joker for sure. When it comes to Jim, Bruce trusts that he has the same code as himself; even in The Killing Joke, after Joker crippled his daughter, Jim told Bruce that he wanted everything done "by the book." Bruce knew that in letting Jim point a gun at Joker, the risk to his life was unlikely. However, none of this applies to Jason. Jason would have 100% pulled the trigger. It's the same as Devil's Advocate; Joker's death was a certainty, not a risk or a possibility. And in those circumstances, Bruce chooses Joker in spite of everything else. He endangers the life of his adopted son by slitting his throat (actually, it's more or less canon he actually killed Jason) to save the life of the man who murdered him. (...Look. I ship Batjokes, but I also like the Batfam and Jason especially, and this makes me feel so bad for him it's insane. Sometimes I think about RHatO #25 and Batman & Robin #20 and really wish I could punch Bruce in the face. I say this as a Bruce fan.)