Fanon : Aang never cared for Katara ‘s ambitions since he was too busy being the Avatar or goofing off. After they married, Katara was nothing more than a trophy wife to Aang.
Canon : Aang has been supportive of Katara since day one. Need I remind you that he offered to take Katara to north pole so that she could also learn water bending. He could’ve easily refused Katara ’s request if he didn’t care about Katara ’s ambitions and go to North Pole all by himself since he had Appa and was already a good enough air bender that he could protect himself. But he didn’t do that because he wanted to help Katara. Also, when Pakku refuses to teach Katara water bending because she is a girl, it was Aang who refused to learn water bending from him because he wouldn’t want learn from a master who didn’t teach Katara and vehemently protested against even if he didn’t have any other source to learn water bending. It is only on Katara ’s insistence that he agrees to it. Even then, he secretly teaches Katara all the water bending moves he had learned, knowing well that this might snatch his only chance to learn water bending. When Katara starts to teach him water bending, he shows all due respect and appreciates her help and is her biggest #1 fan consistently. Also, after her marriage to Aang, Katara was more than Aang ’s “trophy wife”. She was regarded as one of the world’s best if not the best healers, she fought for blood bending to be banned (showing that she was very much active in politics), she taught water bending to the next Avatar. Don’t know how it sounds to you, but to me it sounds like that Aang showed Katara plenty of support and never considered her ambitions or needs to be beneath his.
Fanon : Aang never gave enough consideration to Katara ‘s emotional needs. Katara was the one who had to do all the emotional lifting and she was practically Aang ‘s mom.
Canon : While on surface, this argument might look like it has merit but it feeds off of racist and sexist trope of the mom!Katara that reduces Katara as the “mom” or “caretaker” of the group with her emotional needs never taken in consideration. The thing is, that Katara has had to look after everyone ever since her mom’s death and her father leaving the tribe for war. She is expected to do all the chores, look after her brother Sokka and the war forces her to grow up and become more mature than a child her age should be. However, that doesn’t mean that Katara providing verbal affirmations to Aang when he’s feeling sad is to be seen as her being the “caretaker” in the relationship. They’re friends and it is pretty normal to want to cheer up your friend when they’re feeling sad. Plus, those kind of interactions aren’t the only kind of interactions Katara and Aang have. Often times, it is Aang who makes sure that Katara has fun like penguin sledding with her, amusing her with his antics, gifting her a hand made necklace and going to a mountain top to bring a rare flower (the plan might’ve failed because of the volcano but the emotion behind it stands) speak volumes just how much Aang wants to make Katara happy. It is by Katara ’s admission that Aang brought back something that had been missing from her life : fun! That’s why she likes Aang so much; he knows how to have fun and she doesn’t have to pretend to be the “mature” one who is expected to not do any kind of child like activities and have fun. My point is, Aang never treats Katara as his “caretaker” and Katara had plenty of fun in Aang ’s company and let go of all her burdens, even if it is for a moment.
Fanon : But Aang stopped Katara from killing her mother’s killer! Zuko fully supported her and he is the only one who understands Katara ‘s trauma of losing her mother. Aang is always trying to force his principles on Katara.
Canon : Umm, technically Aang didn’t stop Katara from killing her mother’s killer. He wasn’t even there when Katara, on her own, decided to not kill her mother’s killer. Aang only expressed his anxiety because he knew the toll of killing a person couldn’t be borne by Katara (and she is just a kid! The fandom loooooves to forget that, don’t they? They just want to a fourteen year old to kill someone for their fanon ship,never taking into account how it would affect a literal fourteen year old to have blood on her hands). And even then, he never stopped Katara from going. He gave Appa to her and didn’t try to stop Katara and Zuko even once during their journey because Aang understood that Katara needed to do this in order to gain closure. And it is solely Katara ‘s decision when she decided to not kill that man. And as for understanding Katara (and her trauma), Aang gets it how Katara feels because he’s been there. He’s a genocide survivor and he lost his culture and all the people he had ever loved and he was so angry and upset over it that he entered in Avatar state and was only bought back when Katara told him that she and Sokka were his family. Aang has already been in Katara ’s place (not that their traumas are identical or that either ’s trauma was interchangeable or anything like that) and knows the anger, resentment and grief that Katara feels. Also, in that episode, Zuko doesn’t go with Katara just because he has sympathy for Katara ‘s grief but because he wants to be in her good books since at that time she was the only one in the gaang who didn’t trust Zuko. He doesn’t understand the mental state Katara ‘s in and how Katara would be affected. He is only focused in winning Katara ‘s trust back so that he can be fully be a part of the group. At the end of the episode, he is the one who admits that Aang was right and that violence is never the answer. I know it sucks for fans to admit that Zuko was in the wrong but it is true that Zuko was kind of an asshole in the episode.
Fanon : Katara never returned Aang’s affections. It was one-sided.
Canon : Yeah sure, kataang was so one-sided. Remember when Katara and Aang kissed in the Cave of Two Lovers? Remember when Katara and Aang kissed before Aang went to face Ozai on the day of black sun? Remember when Katara kissed Aang after the war ended? Remember all the times Katara kissed Aang’s cheek, something she doesn’t do to anyone else on the show? Remember how devastated she was when Aang died and how glad and happy she was when Aang came back to life? Remember?????