"Why do so many people (zutara shippers) dislike Aang?"
The simple answer is that Aang doesn't change.
We the audience are told that he is a dynamic character (ex. when Katara tells him she's proud of him during the Day of Black Sun on top of the submarine when he kisses her) but that difference is never really shown. He reacts pretty much the same way to difficulties thrown his way throughout the entire series. His first response to problems is to go into the avatar state, thereby putting everyone around him, including those he cares about, in danger. He does this when finding out about the Airbender genocide, when confronting the sandbenders who took Appa, and threatens to go into the avatar state when the Ember Island Play version of Katara doesn't return his romantic feelings. I don't necessarily even blame him for the first two instances, but his continued lack of regulation for his emotions makes him somewhat unlikeable, especially when he never apologizes or changes his behavior.
His treatment of Katara in particular is noteworthy here and justifiably annoys a lot of Katara stans (such as myself) because whenever he is in a good mood, he's a great friend to her. He compliments her waterbending, tells her she's an amazing teacher, and stands up to Master Pakku for her. But the moment he's in any way inconvenienced, he's immediately yelling at her about his issues, most of which have nothing to do with her, when all she's trying to do is help. His constant refusal to understand or sympathize with her problems is also very upsetting, because he goes on for several monologues (ex. before the non-con kiss in Ember Island Players) about how challenging things are for him, but never apologizes to her for his outbursts, or offers a safe space for her to talk about her problems. The result is that all of the emotional labor in their relationship (which carries over into Aang's relationship with Sokka and Toph as well) is done by Katara. She is always the one making the effort to appease him or help him feel better, and the relationship therefore comes across as imbalanced or unfair to Katara.
And notice that most of the instances of his lack of regulating his emotions that I've listed are in the latter half of the series. Aang yells at Katara about her not understanding the pressure that he's under (failing to see that she is the last southern waterbender and has also irrevocably tied herself into his quest of ending the war) in the first episode of the finale. His treatment of Katara arguably gets worse throughout the series. And beyond just his relationship with Katara, he's confronted many times with the way his avoidance of his problems/ running away has hurt people, and yet he continues to do this as well in the finale episode, running away from the group after their argument in the beach house courtyard about how he can't kill Ozai, even though the narrative tells us that this tendency to run away is resolved in The Storm, which is in the first season.
Besides how his lack of change continuously hurts the other characters, particularly Katara, and goes without consequence or is left completely unaddressed, it is also just straight up annoying to watch. The nature of fiction is that a character goes through some kind of conflict, learns something about themselves/ changes, and uses those positive changes to face a larger problem, coming out on top because they have evolved as a character. But when a character's problems are consistently ignored, like when the entire guru plotline of him having to give up Katara was scapped just for him to master the avatar state by complete coincidence in the finale, it's frustrating for people with media literacy to watch. The narrative seems to go out of its way to make sure Aang never has to contend with the bad things he does, or at least never has to make any meaningful personal changes because of them, like when Aang burns Katara in season one but she is never angry or upset with him because she magically learns how to heal right after. And to be clear I'm not holding Aang to the standard that I would a real twelve-year-old, because, again, that is the nature of fiction: Characters have to suffer, grow, and mature, and when they don't, they aren't entertaining or moving to watch. Aang isn't a real twelve-year-old, he's a character who never has to change because the narrative doesn't make him. And when compared to a character like Zuko, who admittedly has made much worse mistakes, but consistently apologizes for them and changes as a result of them, Aang's character arc simply falls flat.
I think rabid Aang Stans and zutara antis fail to realize that zutara shippers are totally aware that Zuko is much worse than Aang for like 80-90% of the series. But Aang always stays the same, even when he's hurting the people closest to him, like Katara. And Zuko genuinely makes an effort to change and make up for his past treatment of Katara, which is why that last 10-20% of the series matters a lot more to shippers than the other 80-90%.
