I'm back, for more discussion of Azula
Here is my opinion of the main factors to Azula's downfall:
Ozai:
I think that we can safely say that Ozai deserves a lot of the credit for how Azula turned out. It seems likely that he was the one who pressured her, right from the begining, to become who she became. A large part of Azula's character that is often passed over is her insatiable need to please Ozai. The hints are small but they are definitely there - gestures such as re-naming Omashu after him, risking her life to protect him in DoBS. The last one especially - it seems apparent that she really cared about her father. When he appeared ready to abandon her in "The Phoenix King", it really threatened to be the last straw, but Ozai made up for it by amking her Firelord. That gesture apparently meant the world to Azula - she spent some time in the throne room obsessing over the need to live up to her father's expectations, and become the greatest ruler in Fire nation history.
So Ozai played a two-fold role in Azula's situation - his influence on how she was raised, and in inspiring her obsessive need to please him, to the point where she began to snap under the pressure.
Ursa:
Ursa's influence on Azula, or, rather, lack of it, shares most of the credit with Ozai for how Azula turned out. How Ursa actually felt about Azula is rather irrelevant - the fact is that Azula was convinced that Ursa hated and feared her and thought that she was a monster. This no doubt played a huge role in convincing Azula that her mother was right about her being a monster, and drove her even further under her father's influence.
I think that her failed relationship with her mother lies at the heart of Azula's problems.
Mai and Ty Lee:
Mai and Ty Lee's betrayal was effectively the catalyst that began Azula's slide towards insanity. Azula's entire being was founded upon the principle (developed by her mother's rejection) that love and trust are for fools, and that fear is the only reliable method of maintaining loyalty. When Mai and Ty Lee betrayed her, they proved this wrong. One of the central principles in Azula's entire being had been shattered. That had a huge effect on her.
I'm feeling really tired at the moment - I'll post more about this tommorow.