The third reason to stay out is that we know how hard getting out is. Bombing ISIS on behalf of the Iraqi government may not change the balance of power in Iraq very much. If we again prop up a weak government, we may simply delay the day when Iraq develops a political system that matches its domestic balance of power. That seems likely to be a long, drawn out violent process that our participation may only delay.
In a way, the President is now a victim of his own exit strategy. As with Afghanistan lately, he tended to claim that we could leave Iraq because of the success of the state we were building. Staying out may require surrendering that pretense. Better to admit that Iraq is worth far too little to us to justify the sort of effort required to repair it and that we don’t know how to do that anyway.