I’m not sure if my reasons will be the same as the OPs (and feel free to tell me to back off if I’m overstepping) but I live my fandom life perpetually prepared with this essay so here we go.
The thing is, from the very beginning Kataang is an incredibly one-sided pairing. You get to see Aang’s feelings from Katara all the time, but outside of three isolated incidents (in sixty plus episodes, they really had no excuse) you see nothing from Katara that even hints she might reciprocate his feelings, or that her own motherly feelings for Aang ever changed into something different. (She kisses him on the cheek the same way she kisses Tom-Tom, a literal baby, and what is probably one of the most powerful shots of the entire series features Katara holding Aang in the famous Pieta pose. They really should have toned down the motherhood vibes if this was the pairing the intended from the beginning, that’s all I’ll say about that.)
People frequently site The Fortuneteller (or, rather, the last twenty seconds of the episode) as ‘evidence’ for Kataang, or that she was starting to consider him in that light. This would be fine, except for the fact that a) Katara’s actions and feelings towards him do not change after this, and b) the entire rest of the episode seems like it is foreshadowing Aang’s future character arc and explicitly not Kataang. What I mean by this is, the episode itself features a young girl with a crush on Aang that is deliberately and explicitly paralleled to his crush on Katara. Meng has marginally more self-awareness than Aang (for which I’ll given him some leniency, here, because he is twelve and spent a hundred years as an ice cube) and realizes that he doesn’t return her feelings. This is incredibly important because the episode tells us that’s ok–Meng herself realizes that Aang just sees her as a friend and that he has feelings for someone else, and she just wants him to be happy. This is an incredibly important message for any show, especially one aimed at kids, but I can’t help but feel like it’s severely undermined at the end by Sokka’s oddly placed ‘that kid is one powerful bender’ and Katara’s seeming ‘consideration’, because that… really isn’t the lesson that this episode should have ended on.
(But really, I mean, saying the Avatar is a powerful bender is a little like saying water is wet. You know who else is a powerful bender? Toph, the most powerful Earthbender in the entire series. Azula, a firebending prodigy. Zuko, especially after training with the dragons. Not to mention that Aunt Wu was kind of a fraud, and the secondary theme of the episode seemed to be ‘you can’t rely on other people to tell you your own destiny’. Unless you’re Katara, I guess. This makes me mad in particular because Katara is my favorite character, and she was so badly shafted by the way this episode ended and what it represented for the series as a whole.)
Which brings me to how Kataang, as a ship, is detrimental to Katara, specifically. I try to ignore the existence of the comics, but it’s hard when so much of it is borne out by the way Katara is sidelined in LoK (yes, I know LoK wasn’t about the Gaang, but even the cabbage merchant got a statue, where the hell was Katara’s????? and why wasn’t she present in the Gaang flashback about a bloodbender’s trial, when she was the one who got bloodbending outlawed and would have been the best equipped to contain him? When Aang, Sokka, and Toph were all in that scene?). And in the comics, Katara just… isn’t Katara, anymore. There is one panel in particular that I think kind of perfectly sums up how heartbreaking their relationship is, and it’s the one where Aang is having a great time showing off for his Fanclub, and Katara is…. in the corner. Curled up with her head on her knees, looking forlorn and completely alone.
And she apologizes for it.
Even if you ignore the comics, though (and you really should, they are awful for pretty much every character, especially the gaang),there are a lot of things in the show itself that make it seem like Katara is, at best, settling, in spite of her own true feelings. Again, there’s the fact that their ‘relationship development’ is one-sided, with Aang’s feelings for her explored but not the other way around. There’s also the fact that it’s an incredibly unequal relationship emotionally. Now, Aang may get a pass for some of this because he is twelve years old, but then that becomes part of the problem–an immature twelve-year-old boy really had no business getting into a serious relationship with anyone before some serious growing up, and said twelve-year-old boy with a chronic ‘running away from his problems’ problem should absolutely not have been getting into a relationship with an overly-mature fourteen-year-old girl with serious abandonment issues.
(That last part will be important later.)
Katara takes on herself the responsibility of caregiver, especially for Aang. We really don’t get to see her in a position of not trying to bear everyone’s emotional burdens until Zuko joins the Gaang later and shares that task (you’ll pry Momtara and Dadko from my cold dead fingers, but this isn’t about them), but this is especially prominent with Aang. She is there for him constantly. She helps him deal with everything from the genocide of his people to losing Appa, his friend and last connection to them. And Aang is ‘there’ for her insofar as he’s the Avatar, sure, and her hope for the world–but that’s not specific to Katara. And if they were truly going to commit to this pairing, they should have at least had Aang ask Katara about her mother at some point prior to The Southern Raiders.
Even then, he either cannot or chooses not to understand where Katara is coming from. Part of this is, I think, because his development was hamstringed for pretty much the entirety of book three. He was never allowed to grow past parroting the monks and their advice (rather than doing what Zuko does with Iroh’s advice, which is internalize it and learn from it and then apply it, and even if he can’t quite put it into a neat little soundbyte he shows he understood and adapted to what he was told), which does make sense from a certain perspective (because, again, he’s twelve years old and woke up a hundred years on to find that his entire people were gone)… except that the narrative never tries to say he’s wrong. In fact, this is a serious problem I have with book 3 in particular–Aang’s development was stunted because the narrative would not let him be wrong. Even the framing of TSR tries to bear this out (the commentary for the episode, as I recall, tries to paint Aang and Zuko as the angel and devil on Katara’s shoulders, which is so wrong for so many reasons–thankfully the bulk of the episode, outside a few incongruous one-liners, doesn’t really support that reading), but it only goes to prove that Aang may remember the Monks’ teachings, but he didn’t fully understand them. He couldn’t! He didn’t get a chance to learn! Monk Gyatso was found amidst a slew of Fire Nation corpses, proving that he didn’t just lay down and die but went down fighting to protect his people, and yet Aang never stops with his ‘the monks think all life is sacred’ bit.
And, ok this is a bit of a tangent, but no, I don’t think Aang should have killed Ozai. He was twelve years old, he shouldn’t have been killing anyone. But I believe the show should have given him an actual character arc, rather than tossing a deus ex lionturtle and Rock of Destiny at him so he never had to have his beliefs or idealization of the Air Nomads challenged in any substantial way.
But back to my main point–Aang never helps to share Katara’s emotional burdens. He is also, as I mentioned earlier, someone with a chronic running away problem–this culminates in everyone believing he did just that right before the Big Battle, because he stormed off and Katara had no way of knowing if he’d even come back. (She had faith that he would, but she was concerned, too.) Again, this wouldn’t be a problem if it were a) presented as an issue he would need to work through, and b) not a defining characteristic of the boy who is evidently supposed to be endgame with the girl with severe abandonment issues. (Not to mention how badly both Aang and Katara were presented in LoK–Aang really just fucked off for months or years at a time with his airbending kid, leaving Katara to sit at home raising the other two who would grow up believing their daddy didn’t love them??? And she just let him do it?????? #NotMyKatara)
As to how this relationship is detrimental to Aang (other than the comics and LoK nonsense)? Just take a look at book 2, when he’s trying to learn Earthbending from Toph. Katara constantly coddles him. Much of the time, she’s afraid to be anything other than gentle and understanding with Aang–partly because of her fear that if she pushes him too far, he’ll run away. (Which he does, several times.) But sometimes, what Aang needs to grow is a sharp kick in the slats, which Toph was more than willing to provide–and which worked. Katara was great for teaching Aang to waterbend, but he needed more than that to grow as a person. And he can’t get that while he’s in a relationship with someone who will apologize for getting upset when he was very explicitly neglecting her. (Sorry, it always comes back to that panel for me, it makes me so mad.)
Anyway, uh, tl;dr: Both Katara and Aang are hampered, narratively speaking, by being placed in such a one-sided and unequal relationship. I didn’t even get into the forced EIP kiss, or how it was not good that the entirety of their relationship development (going from ‘you kissed me and i explicitly did not like it’ to ‘we’re in a relationship now’) happened off-screen (the EIP scene was their last one-on-one scene together before that epilogue, and they proceeded to spend the show’s emotional climax with other people), because this essay was getting long enough. But in short, they are very poorly matched for two people we’re supposed to believe were blissfully happy and never had any problems for seventy years.