ATLA fandom: Aang tried to force his ideals on Katara and stop her from confronting her mother’s killer.
ATLA episode transcript: Katara: Don’t try to stop us. Aang: I wasn’t planning to. This is a journey you need to take. You need to face this man. But when you do, please don’t choose revenge. Let your anger out, and then let it go. Forgive him.
What’s funny is that Katara said herself she will never forgive him and that’s okay. Aang was fine with that and he accepted that. The whole thing was that Katara was not gonna let anger get the best of her. She didn’t need someones life on her conscience at such a young age too. Bryke pretty much explains this but fandom likes to be that dramatic.
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I would argue that Aang did get it. He found out his entire culture and everyone he knew and loved - except Appa - had been murdered by the Fire Nation. Including Monk Gyatso - the closest thing to a father he would ever have. Aang understood.