Azula's opportunities to kill Zuko (that she never took)
Many ATLA fans claim "Azula was always trying to kill Zuko." However, a cursory examination of the series reveals that Azula had many opportunities to easily kill Zuko that she never took.
"The Chase"-During the Azula vs. Aang vs. Zuko battle, Azula disables Zuko and renders him unconscious. However, instead of taking a half second to finish off her helpless opponent or at least make sure he can't get up, Azula ignores him to continue her chase of Aang.
"The Crossroads of Destiny"-Azula captures Zuko. Instead of killing him or torturing him or anything like that, she leaves him unharmed.
"The Crossroads of Destiny" through the Day of Black Sun-Azula probably could have easily have had Zuko covertly killed off, especially before the Fire Teens return to the Fire Nation. She had the whole Dai Li working for her, after all. And who would have cared if the disgraced, banished prince "accidentally" fell overboard and drowned? Instead, Azula makes Zuko a war hero.
Boiling Rock, Part II-Azula could easily have ordered the gondola lines cut so that Zuko, Sokka, Hakoda, Suki, Chit Sang, and the Warden fell to their deaths in the boiling lake. That would have been the easy thing to do. Instead, Azula took the much more risky route of trying to capture the escapees herself. It was the Warden who ordered the lines cut, a decision which nearly killed Azula and Ty Lee.
Sozin's Comet-After Azula's lightning disables Zuko, she could have easily finished Zuko off. Katara was forced into hiding, and it would have taken only a split second for Azula's comet-enhanced firebending to seal the deal, while Azula's dialogue suggests she knew or believed that Zuko was still alive. However, she leaves him alone, and her comments suggest that the idea of getting him medical attention has at least crossed Azula's mind.
If "Azula always wanted to kill Zuko," why did she avoid killing him at so many clear-cut opportunities?