No one hides his medical history without a reason. My best guess is some kind of psychiatric history a la Thomas Eagleton.
It's about control. If there's something in his past Obama doesn't want people to know, one way to maintain control is to withold everything he possibly can. Or even if there isn't, like any politician he wants control.
If Obama's not required to divulge things, he won't. If he can get away with presenting a carefully crafted image of himself and revealing nothing else about his life, he will.
It's a politician's dream, isn't it? But most pols can't get away with it.