Ok look I’m just gonna put this out there…Sokka was the oldest male in the Southern Water Tribe, right? That’s why he was the warrior and all that jazz. Katara grew up with a bunch of old women and girls and little boys. So when Aang came along and subsequently showed interest in her, yeah, I’m not surprised they had a thing. But even if they did love each other, he was her first love. Many would call that a childish love, especially considering he was probably her first romantic love interest.
Then comes along Zuko, someone she had to hate right off the bat because he was a lil crazy (I mean, understandably) and chasing them around the world, trying to kidnap her friend/possible romantic love interest. But then things change. We see that change in the show. And when the two of them are stuck in the catacombs of Ba Sing Se, we see her attitude towards him change rapidly. Because now she’s gotten out of her childhood home and has been places and met people and learned that not everything is as simple as it once seemed. So here’s this guy that she previously hated, now opening up to her and actually trying to be a decent person. He suddenly does a 180, shattering that fragile trust she had gained in him. And it sucks.
But then Zuko goes through his metamorphosis. And Katara experiences a supreme amount of loss and struggle. She herself realizes that not every person’s history is black and white (shoutout to you, Hama). I’m sure there are tons of examples, but I’m too tired to find and list them.
ANYWAY, when Zuko comes back, apparently a changed man, it’s not surprising that she’s skeptical. She gave him the chance to prove himself before, and he failed. But then he does prove himself a thousand times over. And Katara has the life experience to understand how significant that is.
Aang is a great guy, but he’s so straight. He never really wavers in his character or morality, at least not to the extent that Zuko does. Katara helps Aang in so many ways with her kindness and strength and generosity. But to me it just seemed so one-sided (again, I’m sure there are examples that counter that, but overall it just seemed one-sided). The fact that Katara is able to find it in herself to forgive Zuko, and the fact that Zuko is deserving of forgiveness, and the fact that they help each other grow, is monumental.