Because it's rather unfair to have the oppression of Islam forced on you. I wouldn't like living in a Muslim country and being banned from drinking alcohol. No reason the Christians of Iraq should as well.
Pretty much everyone agrees that it's a good thing our Constitution bans a state religion. So why wouldn't it be in Iraq?
Because people in America are not the type who let their religion dictate their whole life. Given how staunchly Muslim the people are in the Middle East, I don't really see how you're going to get them to agree on a constitution that doesn't include Islam in at least some way.
I thought the point of our being in the Middle East was to spread democracy (you know, the thing where the majority gets to say what happens), not Christianity. We
have gotten past the Crusades, haven't we?