Part of Zuko wanted Katara to kill the man, wanted to shout out and demand it of her, of his...he didn't know what to call her, for they hadn't discussed their relationship (or lack of one?) before he was nabbed. He did not, though, for he quickly realized that was the side of him associated with Sozin's blood lust, of Ozai's, that was speaking. And the prince no longer wanted to be associated with that sort of attitude.
He was not that uncaring bastard that had stormed Katara's village looking for the Avatar. No, not anymore. He'd changed. He had.
Stepping up to the waterbender, he put a hand on her shoulder. Without breaking the cold gaze he couldn't help but continue to direct at the professor, he told her: "Don't drop to the levels of my nation. You're better than that."