Zuko tells Katara she hurt him in the Catacombs, but she didn't do anything?

See, that's kind of the point: she didn't do anything.

The Crossroads of Destiny episode is a barrage of emotions, plotpoints, and gutpunches, one right after the other. It's logical, given that right here is where all the crossroads (pun intended) for the characters involved take place. But I digress.

Literal thousands of words have been written about Zuko and Katara's interaction in the Crystal Catacombs, as well as Zuko's subsequent betrayal (which wasn't as straightforward as most people think—more on this later). However, I've seen very little discussion regarding one of the things I find most intriguing about CoD: the non-collision of glances.

One of the things I find most fascinating about CoD is this interaction, because it's easy to focus on Katara's longing/regretful glance—the fact that she looks back in the first place—and miss that, because he's looking away, Zuko doesn't know she was reluctant to leave.

And it seems like something unimportant, small in the scope of everything that's happening; but when you think of Zuko's state of mind during this scene, that missed glance gains so much weight.

During the rest of the series, we witness a lot of Katara's feelings regarding CoD, but don't see much from Zuko beyond his guilt and regret. So let's try to revisit that experience through his eyes.

What did the Catacombs mean for Zuko, personally?

Openly sharing his grief about his mother for the first time in the entire series. Reaching out for the sake of another person, and having them reach back. Not only that, but he was also offered what amounts to a miracle, something Zuko only ever dared wish for in a literal fever dream: getting rid of his scar.

It's in the Catacombs that he allows someone to touch his scar, something we don't ever see happening before or again until S3. This is undeniable evidence of Zuko's chosen emotional vulnerability during CoD.

And what does the waterbender do with this connection—with her promise to heal him?

Ignores it.

When Aang and Iroh burst in, the very first thing Katara does is rush to the Avatar. Zuko's reaction? To stare in confusion and dismay. He laid his emotions bare, was thoughtful and contemplative—not even snarling at the Avatar before or after Aang snaps at him. He just seems...lost.

Weren't you hoping I'd turn against my family and nation out of gratitude? Didn't you think that if you made me feel like I was special, I'd refuse my only chance to go home to run away with you? Zuko...you can't possibly believe... What am I supposed to think, then?! That you suddenly forgave the man who hunted you across the world? That you'd heal my scar for no reason other than empathy? That for a delirious moment you cared about me?!

(...)

You promised, Katara. You took out that stupid spirit water and said you'd been saving it for something important and then offered to heal me, and I thought...it made me... For a second, you made me feel like I was that something important. And I'd never... But then the Avatar showed up, you jumped into his arms, turned your back on me, and left without a second glance.

This scene in The Block explores (rather clearly, I believe) what I think would've been Zuko's thought process during this scene. Mainly, coming up with a reasoning behind Katara's behavior that made sense to him.

The idea of the betrayal in CoD flowing both ways is enthralling to me, because it depends their conflict even more than we see in canon. It also brings Zuko's upbringing into the game, and shows us the subtle consequences it has in his psyche.

But beyond all that (and regarding Zuko's betrayal of Katara in the Catacombs) there's a little truth in this headcanon.

Because Zuko didn't promise that he'd choose to join the Avatar and fight by her side—but Katara did offer to try to heal him, and then left without further word.

To Zuko, who has been lied to and manipulated so many times in his life, that sort of promise/refusal back and forth must've felt familiar. He rationalizes that Katara wanted him to join the Avatar and used the promise of healing as a reward, a bait.

Which she didn't, of course; the reluctance to leave Zuko is evident in her body language when Aang rushes out of the Caves.

But Zuko has no way of knowing that, because he himself was looking away, having already decided that Katara would break her half-made promise. Because, really, why would she follow through? He's a failure, her enemy, and he doesn't deserve healing.

Ironically (or perhaps naturally) accusing her of this is what allows Katara to start forgiving him in The Block. It proves to her that he was hurt by what happened, too, and confirms that he hadn't lied to her or tried to trick her into lowering her guard in the Catacombs. He had been vulnerable, genuinely vulnerable, and it makes all the difference.

This misunderstanding opens the way for honest, healthy communication regarding what happened under Ba Sing Se, which is something I would've loved to see in canon.

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