I hate when people reduce Aang being upset about the play in EIP to just being about his feelings for Katara. Was he upset about that? Absolutely. Was he also upset about the overall portrayal of himself as a person? YEAH.
I just think people use this episode too easily as a major anti-Aang moment without actually considering what he's feeling. Aang isn't just being a jealous "nice guy" (I also fundamentally disagree with the idea that a 12-year-old can even be a "nice guy") when he sees the play portraying him and Katara as having a sibling relationship and her having feelings for Zuko. It's much more complex than that.
Aang is about to fight the Fire Lord (at TWELVE) in order to end a war that has been raging for the last 100 years and has resulted in the deaths of all of his people save him, Appa, and Momo. He is obviously feeling a LOT of stress and anxiety about it, and the one thing that has kept him grounded from all of his heavy emotions is Katara. And I don't mean that in the "he puts too much on her" kind of way that so many antis love to think. Katara is caring, and she and Aang have a reciprocal relationship. He supports her throughout the show, just as she does for him. We just see her do it for him more because, well, he has a lot more on his plate with waking up after 100 years to find his whole culture and nation dead and the knowledge that he has to master three elements within a few months and then fight the most dangerous person on the planet before he destroys the world, no biggie. So, he's feeling all of these emotions, and all he wants to know before he potentially DIES (again) is that the person he loves, loves him back. His reaction, while we don't have to agree with it (at least the kiss, because I think his being mad about the play is valid), is understandable. This is a, once again for emphasis, CHILD who is feeling some very complex emotions (and has been since he woke up).
Also, the whole play is propaganda, and I think not enough people talk about that (at least on that side of the fandom). Aang is played by a woman, which is meant to undermine his status as a figure of power and as Katara's love interest. So not only does he have to watch as Katara and Zuko are put together (a very sexualized Katara, I might add), but he is watching it be done at his expense. The Fire Nation has already stripped him of his people and culture, and now they are stripping him of his "masculinity" and his love. How is he not supposed to be upset about that?
Yes, Aang is jealous. Yes, he reacted badly to that jealousy. But if you truly think that Aang's only issue is that he's jealous, you are being willfully ignorant. His feelings leading up to him saying he would "be in the Avatar State" are much deeper than just "Katara might not like me back." They are 100% a factor, but even then, as I've already explained, his feelings for Katara and why he feels so strongly in that moment are more complex than just straight jealousy. He's afraid, he's stressed, he's angry, he's still grieving, he's desperate. Using this moment of high emotion as the main example of who Aang is as a character is stupid. We clearly see by the end (and even in the moment when he chastises himself) that he is very aware of how his actions were wrong and how he has reflected on and grown from them. When he walks out onto the balcony in the last episode, he is fully ready to accept being alone. He does not force Katara to walk out there; that is a choice that she makes on her own.
It's just crazy how Zuko (who is four years older than Aang) is allowed to be complex, to mess up, to have negative emotions and reactions, and to lash out, but we all must forgive him. But when it comes to Aang, he is held to a significantly higher standard and is given no grace by certain portions of the fandom. Oh, you think Aang sucks because he got jealous and acted poorly as a result? What about Zuko in The Beach? Zuko, who was throwing things, yelling at Mai, and being overall controlling, is someone we can forgive and see as a "better" partner for Katara, but Aang is never allowed to grow from the EIP. And before people say that Zuko "apologized," he very much did not tell Mai he was sorry for his actions. The double standard is just insane, as is the hypocrisy.