J-Man here hear me Roar!

Katara has motivations that stretch way beyond romance. Her willingness to help those in need. Her dreams for the end of the 100 year war and rebuilding the four nations. Her anger towards her dad for leaving them. The fact that she had to grow up faster in ways Sokka didn’t have to(not saying Sokka didn’t have to mature as well but it’s in a different way. Her survivor’s guilt when it comes to her mother. Just because she has such a deep love for…her literal lover doesn’t mean that’s what defines her.

Because they get together at the very end of the original series (after the entirety of the resolution of Katara's confusion and the development of her romantic feelings happens off screen), and every single thing that comes after (the comics, LoK, the movie) reduces her role to that of girlfriend/wife and mother of the Avatar's children.

Kataang haters aren't the ones who reduced Katara's role and importance in the narrative. The comics did that. LoK did that, repeatedly and egregiously. The Consumed by Destiny meta series goes into fairly exhaustive detail using every single scene featuring or referencing Katara in LoK and then the comics, and since that meta was posted, this particular situation has only worsened, to the point where the movie doesn't tell us a single significant thing about her life--not even her relationship status even though, according to the existing timeline and word of god about the character's ages in the film, she should already be married and have at least one child by then--other than a throwaway line about her being a republic city councilor that is never referenced again. (Including in LoK, which in-universe seems odd, but makes sense from a doyalist perspective considering it was almost certainly a response to criticism about Katara's portrayal post-atla rather than any significant rumination on her character and where and who she'd be at that point in her life.)

I think it's important to note that there is no private apology between Aang and Katara after their (rather public) argument.

The only 'resolve' is displayed through a speech that Aang makes to the entire group: "Everyone, I know I've asked a lot of you on this journey. But we're about to accomplish something that will change the world."

Now, the next interaction between Aang and Katara is when she revives him after he dies.

"You're incredible, Katara." He says.

Then the topic immediately shifts to Appa and everyone is there and ready to comfort Aang regarding the bison's disappearance.

It's a damn good thing Katara was able to revive herself and the others. After all, it's very important, apparently, that they continue to shoulder Aang's emotional burdens once more, and not hold him accountable.

("I can't believe I trusted him." - Aang)

Now, at this point, given Aang's history, the supposed 'growth' he's had since the original series, is it a stretch to critique him? To call him naive? To maybe, just a tiny bit, see his relationship with (and reliance on) Katara as something he takes for granted? Calling someone 'incredible' is just words, at the end of the day, especially when you've knowingly placed their lives at risk.

The speech to the group is not an apology, it's a justification.

And he can call Katara incredible all he wants, but complimenting her like that for cleaning up his messes after telling her she doesn't understand feels less like an apology and more like, again, a justification, just like when he told Zuko in the finale that if he got struck by lightning he could just count on Katara to heal him. And, interestingly, that does happen to Zuko, and it causes both Zuko and Katara a lot of pain.

What even is statement this anyway? It's not an apology. It's not an acknowledgment of wrongdoing or a mistake.

It's shock.

It's surprise.

Why is he surprised? What is he expressing besides realization that in hindsight he now understands the lies he believed. And not the lies Taga, the lies he tells himself about this being the magical fix.

The constant search for some magical fix.

The constant striving for the easy way out.

Never wanting to do the hard work.

Somehow diluting himself into thinking because it's risking everybody's lives that makes it the "Hard Work".

And what does he do to rectify it?

Probably nothing. I haven't seen this movie but even if he "does something" we know he doesn't learn. He's made these mistakes before throughout the show and the comics. He never changes his behavior.

Katara:

Katara blasts open the door, the captain starts bending at them, then Zuko jumps in front of her to block the captain's fire. The captain begins to attack Zuko, then Katara stops him with bloodbending.

Which is not to say that Katara's actions are only defensive here, certainly. She went after the captain with intention. It's just interesting, because contrary to what certain people say about this episode, her bloodbending is portrayed as very controlled, not the actions of someone who is acting out of a place of blind rage.

It's also not shown as something that only comes from aggressiveness. The fact that Katara's first act on her own as a bloodbender is to stop the captain from attacking kinda contradicts the idea that bloodbending can only be used for evil.

Also, Katara is just like, so cool here. No wonder Zuko is looking at her like that.

It's also an interesting parallel to Zuko learning lightning redirection as a symbol of redirecting violence aimed at him. Katara seizes the captain's arm as he's about to attack and literally bends it away from them, redirecting his attack into something harmless. Remember that she believes at this point that this man killed her mother with firebending, and she quite handily prevents him from bending with only a few movements here.

We love them outside of canon where they can't be touched.

I beg new Zutarians to open your eyes and not let brats and bandwagon hoppers convince you to drop what makes your ship compelling.

These people do not wish you well!

As a personal favor to me, a community member who’s been here for decades, each time another illiterate, provocative anti pisses you off kindly drop a comment/kudos on a new fic/art work/meta analysis.

We deserve balance.

Aang: [trying to play it cool] So, Sifu Hotman, what's Katara's favorite color?

Zuko: [eyeing the produce] Red.

Aang: [points] Ha! Wrong! It's orange!

Zuko: [examing two cabbages] No, it's red. She told me like two days ago.

Aang: Oh? Do you know her favorite fruit?

Zuko: [paying the vendor] Mango but she enjoys artic berries when they're in season in the Southern Water Tribe.

Aang: [scratches his head] Huh? I could have swore it was papaya?

Zuko: [stares at Aang] Her birthday is in the summer, she has a scar on her left knee that she got as a kid when Sokka pushed her too hard, and she's quite fond of the aroma of fire noodles despite having a low spice tolerance. I know that you’re looking out for your friend, Aang, but I want you to know that you've got nothing to worry about. Katara and I are good friends now.

And I just... They're so close to getting it. They're on the very edge of realizing how underdeveloped Aang as a character actually is and how incomplete his arc was. But the fandom babies and favors him so much that actually making that observation in the main parts of the fandom will never actually be conceptualized, and if it is it will never be accepted.

That's why the fault is being put onto Zuko in this particular instance. They can't admit to Aang's failings as a character so they're looking for a scapegoat to blame instead.