Because he's confused. He's mad about being confused, and it's all because he doesn't know what's right from wrong anymore. It's something his father's to blame for, again, having pushed Zuko to such boundaries by turning against him and forcing him into exile, making him the impression that everything cruel and wrong is, in reality, right.

"Of course not!" he suddenly shouts at her, her words striking a nerve. The flames at the candles spike dangerously high behind him. "You think because I look like this- because I look like a monster- that I am one?"

Zuko points to his left cheek, nostrils flaring with his heavy breathing.

"I am not my father, Katara."