The brave Sir Robin Iraqi Army melted away when the US Army was making its way to Baghdad. That was when Saddam was a fearsome figure, and when punishment for desertion would be ... let's say, uncomfortable.
Today the Iraqi Army is not even sure who is in charge in Baghdad anymore. When ISIS makes their move, the rulers of Baghdad will be on the first (and probably last) airplane out of there, direct to Europe. Who in his right mind would be fighting, killing, and dying for ... for who? For what ideals? They are all Muslims there; and a common man doesn't really care one way or another, as long as ISIS is not too bloodthirsty. (There are some indications that they might be.) That ancient land saw many rulers over many centuries of written history. Nothing of what is happening today is new there. Just another tyrant replaced by another tyrant, same as the old one.
They are NOT all Moslems. There were 2 million Christians there in 2003. Now there are 200,000. These are the remnants of the time when Iraq was one if the centers of the Christian world, with nearly all Christians. The ancient church of the east is still headquartered in Ctesiphon