To understand this cultural divide in the time of "liberation", I propose an analogy:
What if Mexico liberated Southern California? Here you have a white-controlled area where the majority is Hispanic. Throw in another minority (African Americans) in the mix who have constantly been at war with the Hispanics, and oppressed by the whites. What would happen?
Whites would strive to keep their control, and even though they are the smallest in population they have the most resources. Hispanics would claim So. Cal. is rightfully their land, and that the whites stole it from them. Their populational majority would help push this argument. African Americans also have a large community and would not want it to be controlled by the whites (oppression) or the Hispanics (feudal). They would want nothing to do with either group.
In order to understand the correlation you must take it from a cultural divide view - do not take into account all of the other pluralities that would accompany that particular situation as that is a blog in itself --- there are more than two sides/issues to every story.
Moving forward, population differences are not always founded in melanin. Religion is another divider, and there are many more that subsequently form groups.
It is one's inherent means for a survival to belong to a group. In order for there to be a group there has to be another that is different. Basically for there to be an "us", it seems, there must be a "them". In the Iraq of the moment, that need to define by differences seems to be prevalent.
I raise these set of questions to you:
What groups do you belong to?
Do you dislike a certain group because of their beliefs -- and then question why can't we all get along? I personally am guilty of that oxymoronism.
As a resource to find a human perspective on this divide between Iraq's Shia, Sunni and Kurdish population I personally suggest you watch James Longley's Iraq in Fragments. This film is NOT how the United States is destroying Iraq. It is instead a portrait of the human side of Iraq. The trailer can be found below.