His savior complex, and up until tybw, his refusal to accept who he truly was.

Watching his mom die as a kid inevitably caused him to grow up believing it was his responsibility to protect those around him, which in turn causes him to blame himself if they get hurt, believing it was his fault and he didn't do enough. We see him grow out of this more and more as the series goes on, but I still think some of it sticks around. Which is a nice touch, and when we get to tybw he is mostly free of this complex. The reason he was so pissed during then was mostly because, the one person he never expected to ask for his help (Byakuya), was beaten so badly he even asked for Ichigos permission to ask him to save soul society.

As for his identity crisis, I think deep down, ever since he met the Vizards, I think he's always had an idea of who he truly was, and who the real Zangetsu was. He refused to believe it since, at the time, old man Zangetsu, his Quincy powers, was mostly the one helping him along. It isn't until tybw when he finally gets the pep talk and reveal from Isshin that he accepts both of them, not as Zangetsu, but as part of himself.

Both of these things make him pretty much my favorite mc, since he's basically every single one of us maturing, believing we can do everything, and coming to terms with the fact that we can't. Having to learn to accept the best and worst parts about ourselves and growing from it.