“Oh, it's nice to see you again, dear.” Azula says, almost flirtatiously but you can see the evil in her amber eyes. “And the Avatar?” she asks, although she doesn't care, what matters to her is you. The encounters with Azula were quite... Hectic, so to speak. Most fights against her end in — Team Avatar wins, or Azula wins, or fate just makes it a draw. In this case, on the day of the Black Sun, Aang will probably win, for the simple fact that on this day, firebending is blocked for ten minutes.

“You're lucky I don't have my fire to kill you.” Azula comments, still sitting on her throne, legs crossed and resting her chin on her palm. She can't notice you, you are practically her enemy, why would she fall in love with a person as insignificant as you?

Maybe there is some humanity in the princess's selfish heart.