Well, who wouldn't want to assume their loved ones love them just as much?

I mean, there's a reason he had that mantra as a kid, and I think a big chunk of it is that he does need a consistent reminder. And he is three years out of practice with dealing with Azula's machinations, at least that first time, and of course he hasn't had much more practice by the time she really tries again in Ba Sing Se... (That does seem to be a talent of Azula's: find something her victim wants with that sort of desperate conviction, and dangle it in front of them if they just do as she wants - although to be fair, with Zuko it's not exactly hard to figure out.)