I didn't think he's insistant that Aang has to kill Ozai, actually. I mean, Sokka is just as impatient with Aang's holding back when he (Sokka) kills the Melon Lord for him. With Zuko he brings up Ozai after he's just admitted to Aang that violence wasn't the answer for Katara and him in SR, and I took it as a real, genuine question: so then what are you going to do about my father? Because in the end Ozai does have to be taken out decisively--and so does Azula. Zuko can't see any other way than death at that point, I don't think, but then, neither can Aang. The whole challenge that Aang faces--which I love and talked about in my most recent post--is that it's not always so easy as violence not being the answer. So I thought that ep was bringing Zuko to the place where he could understand Aang's dilemma--he could see why just going out and killing somebody might not be a great thing, but they were still facing the problem of having to get rid of Ozai.

With Katara I didn't think he was pushing her so much as agreeing with her. She was angry about what happened to her mother, and Zuko saw how to resolve it. Both of them saw "forgiving" as just letting justice go undone. Neither of them could really understand the concept of forgiving the way Aang did at that point, imo, maybe because of all the ways they're alike. They're both idealists who seem much more bothered about the world not being perfect than Aang is.