It's called villain protagonist's journey to hero. In reality, Zuko's what we called anti-villain. He's still a villain for most of the series mind you, just one with added depth and complexity.I'm kinda with tstorm on this one. He's an /antagonist/ in the first book (since he unequivocally battles against the protagonists and for the 'wrong' side) but he's not really a /villain/-- they're not always interchangeable, and this is a good example.
The Anti-Villain — Definition, Types and Examples
An anti-villain is a character who has heroic personality traits or goals but is ultimately the bad guy in this story.
www.studiobinder.com
Exactly. Somebody gets it and is more thorough.I feel like you're forgetting all the casual terrible things he does early. He's shown as a spiteful, angry child, scorned. Horrible to his kindly uncle constantly, more than happy to order the torch to any civilian settlements which defy him.
Does he have an arc, and move beyond that? Absolutely. But he still sits squarely in the villain square through book one.