Depends on when he signed up. I know guys who never wanted to go to Iraq who signed up for peacekeeping in Kosovo. I'm not aware of when this kid joined up, but if he did so before war was imminent it's safe to say that he didn't sign up to fight in Iraq. That's not saying much, though. The contract he signed is much more broad than that. I doubt that any part of it states that he can opt out of unjust or arbitrary conflicts.
So legally, he has no case. I say that unequivocally. No judge with even the tiniest pragmatic bone in his body is going to let this slide. Ethically, he may very well have some legitimate claim. It depends on the spirit and the letter of the agreement he signed, and whether or not the command to fight in Iraq breaks those. I'm going to go out on a limb and assume that they don't. You either had a snake-oil salesman as a recruiter or you're stupid if you didn't realize that signing up to fight in the armed forces could realistically entail actually fighting at some point. My friends didn't sign up to fight in Iraq, but when the war started their previous commitment compelled them to go, and that was the end of it.