Right now they're actually teaching soldiers to understand the enemy, to see what separates an extremist from a traditional member of the Islamic faiths and so forth ... etc.
They're taught cultural awareness (lots of it) and other things so they can understand and identify with the cultural and other differences before deployment.
However - I understand your point and I agree to an extent. *If* he was constantly hearing people's prejudice or bigotry - that amount of "I hate people like you" from soldiers - with or without them knowing that he was Islamic (Muslim, etc) - would be an extreme emotional burden and likely to make anyone bend or break.
If I was a psychologist and I had a lot of men telling me "I hate women, women are the bane of my existance and I want to kill them all" I'll probably crack rather quickly, regardless of my education and status as a psychologist.
For Hasan I can see this being very applicable - it's not like you have a choice when you're assigned a Dr. If someone had a problem with Muslims, etc, and they were assigned to him then, evidently, their issues are going ot be discussed.
But that might be beside the point - they haven't quite pinned down anything in particular. Maybe he had other issues that haven't even been rumored around, yet.
Sometimes it's just foolish to try to understand the mind of the criminally insane.