The middle east is already heartbreakingly divided and full of conflict as it is (kudos to you anglos)
The relationship between Kurdistan and Iraq is very akin to the relationship between Israel and the United States.
They're an autonomous region with proper representation, they have the right to self govern and allocate funds and resource, all that we ask of them is to respect the sovereignty of Iraq and the authority of the Iraqi government.
Yet time and time again they prove themself to be a bunch of pampered backstabbing cunts, they bit us in the ass after the UN imposed sanctions and our collective ineptitude (the fault was not entirely theirs, though they played a major role) allowed ISIS to get a foothold in northern Iraq. All of this while they continue to blatantly disregard and disrespect the Iraqi government.
A lot of nations are continuously meddling in my country's internal affairs, dividing us even further would serve no purpose but to topple us.
Also, every time the US intervenes in the middle east you only serve to make matters worse than they otherwise would've been.