Anon asked: Do you think Zuko actually wanted to kill Azula during the last agni kai? By trying to redirect her lightning back at her? Because when he saw her crying in defeat, I don't think he ever pitied her before. Well maybe except when she said "my own mother thought I was a monster". So even before that, despite genuinely loving her, he was always jealous of her and thought that she always gained everything so easily, effortlessly, that she had no issues whatsoever
Did Zuko want to kill his sister? No. Was he willing to kill her if he thought it was necessary? Absolutely. The same goes for Azula "wanting" to kill him. Just take a look at how they both act when they're not under direct orders from someone else or on opposing sides of the war.
As a child, Azula had THE perfect chance to get rid of Zuko, and all she'd have to do was literally sit around and wait. Sure, the way she let Zuko know about Azulon's/Ozai's plan was disturbing, but she did let him know about it and saved his life. Years later, she essentially handed him the crown twice (on Crossroads Of Destiny and on The Headband)
Speaking of Crossroads, let's not forget at what point Zuko threw away everything he had (been forced to) build for himself in Ba Sing Se: he saw Azula being cornered by enemies, and jumped in to help her out. And said enemies were Aang and Katara. Don't get me wrong, they're powerful as hell and Zuko knows that, but he also knows that Aang is a pacifist, that they've both saved his life, and that they never killed anyone. Sure, it's a dangerous situation - but it's far less dangerous than if she were facing the Dai Li or even Iroh.
They genuinely bonded on The Beach (in unhealthy ways that involved arson, but hey, that's progress for them). Hell, they had a meal together that episode - does Zuko, the boy who called Ozai a fool in episode three despite having been disfigured and banished him, sound like the type that would swallow his pride, ignore his anger and be all polite to someone he genuinely couldn't stand just so things wouldn't be awkward for Mai and Ty Lee or because it could backfire on him? No! He would have flipped the goddamn table and stormed off! And in The Avatar And The Fire Lord he actually asked her a question when he was trying to figure something out - which is surprising considering he quite clearly feels insecure due to Azula being better than him in pretty much everything, including on their studies - and she answered him, no lies or "What do I get in return?" (she kinda ruined the moment in the end with the comment about his scar, but let's not focus on that)
And then The Southern Raiders episode comes up, Azula attacks Zuko and his friends, and explicitly says she's going to kill him... yet the second he thinks she's about to die, he instantly looks conflicted instead of relieved or even indifferent. I remind you that Zuko was willing to kill a former enemy of the watertribe that very episode, and that if he didn't believe that killing Ozai was Aang's fate he would have turned his own dad into a kebab... yet he didn't want to lose his sister.
Finally, we get the last Agni Kai, with music that makes it sound like a tragedy instead of an epic battle between a hero and a villain. After Azula tried to kill and Katara, he literally needs emotional support when he sees her cry. His "evil" sister is defeated, he is Fire Lord... yet he isn't happy. Because Azula was in pain. That battle truly humanized her in his eyes, and the war ending freed them from their rivalry.
These two supposedly hate each other, but whenever Azula has a chance to help Zuko out she does it, and his hatred/indifference towards her crumbles the second she's in danger or shows any vulnerability.