It's a toss-up for me. The obvious pick is when he's staring at the star map and mutters, 'It's a riddle, and I'm no good at riddles.' That line's raw, you feel the frustration boiling over from years of being told he's a failure. But the one that really sticks in my head is quieter. Right after they leave Montressor, he's on deck and Silver says something about the galaxy offering a fresh start. Jim just watches the stars and says, 'Looks the same to me.' It's not flashy, but that resignation—the sense that he can't outrun his own reputation, that the universe itself feels like a constant reminder of his past—that's the core of his conflict, isn't it? He wants the adventure to change him, but he's terrified it won't.
I think people overlook how much of his struggle is about perception versus reality. The 'riddle' quote shows him doubting his own mind, but 'Looks the same to me' shows him doubting the possibility of change at all. The movie's brilliance is how it wraps that teenage angst in a spacefaring adventure; the quotes work because they're so grounded.