Azula never considered it her own fault that she tortured her brother. She never felt she was to blame for the pain and suffering she inflicted upon so many. She supposed that was how she operated so guiltlessly, remorselessly, when she destroyed so many lives. After all, was she really to blame for having an instinctive sense of self-preservation? Was it her fault that her brother didn't know how to avoid the pain that she had learned to dodge so naturally?
She knew that her father expected perfection, and nothing less. So she strove to perfect everything, because without everything you were a failure, and a failure would not be tolerated.
Her father felt perfection was above everyone else. He felt that everyone should know this and those who were perfect should be the ones to remind them. So Azula did what was expected of her. She tormented those who were not perfect to remind them of their inferior status. They were below her and she had to remind them.
It was a short time after she reached the perfection she knew she had to achieve, that Azula realized what she was. She was Daddy's perfect little weapon. Never daughter, always weapon. Necessary, important, reliable, but ultimately, disposable. As soon as she realized what she had truly become, she realized that the moment she stopped doing her job, she would be less than perfect, and she would be disposed of, just as the weapon that stops working.
So she continued to operate perfectly because she knew that's what she had to do to stay alive. She continued as this weapon, (this monster, whispered a little voice that was crushed in her quest to remain perfect.) because she knew she had to, and what other choice was there?
Her mother's disappearance meant nothing to her. Her mother never showed the same faith in her as she showed for her brother. So when she left, why should she feel? The perfect weapon does not mourn the loss of one who does not wish to wield it.
By now she was beyond feeling. What was left to feel? The only thing that matter was victory, and she and nothing left that she had not yet triumphed in. Yes, she was the perfect weapon. As lethal, dangerous, and unfeeling as the lightening she could now control.
The Day of Black Sun is the day of her failure. She is placed in battle no different then a soldier who cannot firebend as the best of times. When a weapon is out of ammunition, it is discarded. As the opposing forces approach, she knows her time has come, but she shows no fear. A perfect weapon does not show fear, even when it knows its end has come.