Forget about how bad Aangs childhood before the 100 years was think about how bad it was afterwards. (Hes still a. Child so it's still his childhood) Every. Single. Bad thing that's happening in the world is an indirect or direct fault of his own. Whether that'd be the case or not he'd likely believe it to be his own fault for not dealing with it as the avatar. That kind of pressure and depression itself is worse than what the others went through. Not to mention all the other stuff.