Zuko and Azula have the most fascinating relationship in ATLA
Sibling rivalry is often a trite story of one sibling hating the other out of jealousy. On the surface, the Zuko and Azula may look that way. They have no problem blasting fire and lightning at each other and both of their parents had a favorite. But there’s so much more to it.
First of all, I would argue that in spite of many near-fatal encounters, they don’t necessarily hate each other. It’s far more complicated than that. How they view each other is closely tied to how they view themselves.
For most of Zuko’s life, Azula is the standard he’s held to. She’s ambitious, ruthless, and a prodigy. No matter what he does, he can’t earn their father’s approval like she can. And she rubs it in his face constantly. When Azula is cruel to Zuko, Ozai affirms that she’s not wrong to do so. Zuko rarely argues with her because he’s been conditioned to believe she’s right. Zuko has internalized the blame for how his father treats him rather than project it onto Azula, and accepts how she treats him as normal. He has plenty of bitter feeling toward her, but none quite as clear as hate.
Azula’s view of Zuko is even more convoluted. The first time we see Azula, she’s smiling because their father is about to burn him. The next time they meet, she berates him for being a failure of a son. It looks like she enjoys watching him suffer.
But when Zuko helps “kill” the Avatar in Ba Sing Se, we get to see them in a new context. In the rare moments that they aren’t pitted against each other by the ever looming presence of their father… they actually get along fine.
Every time Azula appeared happy to see Zuko suffering, it was at the hands of their father. It wasn’t just that Ozai hurt Zuko, it what that Ozai hurt Zuko and not her. Every time Ozai insulted or injured her brother, it cemented Azula’s position as the favorite child. And she had to stay the favorite child because she’s seen what would happen to her if she wasn’t. Deep down, she knows just how conditional her father’s positive regard is. When Ozai leaves her in the Fire Nation while invading the Earth Kingdom, the first words out of her mouth are “You can’t treat me like Zuko”. Being better than Zuko is part of her identity.
When Zuko defects from the Fire Nation and begins to succeed without meeting, or even trying to meet, the standards set by their father, it throws her priorities into doubt. In her mind, Zuko is supposed to fail. But she isn’t truly unnerved until she’s betrayed by Mai and Ty Li.
She is incapable of understanding why Mai would chose Zuko, and this drags to the surface her inability to understand why her mother preferred Zuko. She believed her mother loved Zuko and not her. Now Mai, her closest friend, loves Zuko and not her.
This conflicts with her entire view of the world. She sees the worth of a person as equal to their quantifiable skills and accomplishments. She has been admired, respected, and feared, but as far as Azula believes, no one has ever loved her. She was a prodigy who did everything right, while Zuko was the family screw up. Yet people loved him and not her.
For years, being better than Zuko was how Azula measured herself. Ozai said Zuko was lucky to be born. That he was worthless, weak, disrespectful, and both his children believed him. When Zuko left, he finally saw that Ozai was wrong about him. When Zuko returns during Sozin’s comet, Azula too is forced to see that her perception is wrong.
Zuko has become the embodiment of everything she lacks. She thought he was weak, but he’s not afraid enough to fight her fairly as an equal. She thought he was dishonorable, but really he was independent enough to break away from their father’s control. She thought he was worthless, but he’s found people who care about him in spite of his flaws.
Azula isn’t just trying to kill him, but everything he represents. And when she can’t, she breaks. Zuko is still standing. She has nothing left.
Word of God (Bryke) confirmed that at the end of the Agni Kai, Zuko felt pity rather than hate for his sister. This continues into the comics as he genuinely tries to help her. He knows that while she may not have been overtly abused like he was, she was raised in the same web of lies, agendas, and violence.
Their past left them both unable to trust people. Azula controlled everyone around her with fear. Zuko shut other people out and tried to do everything on his own. It isn’t until Zuko has left his old life behind that he slowly begins to let people in.
While Azula hangs onto the beliefs of Ozai and the Fire Nation, Zuko can see their situation from the outside. He sees two screwed up teenagers who spent their lives fighting their father’s war, manipulated into a conflict that isn’t their fault, forced to kill each other over choices made a century before they were born. It took Zuko years to figure out the hell that was his home life wasn’t his fault, but only a few minutes to see that it wasn’t Azula’s either.