Tim Arango reports on the sectarian and ethnic conflicts, exacerbated by the Shi'ite militias going to war on the Islamic State, here.
The Ottoman vilayets of Basra, Mosul, and Baghdad were spatchcocked together by the British, who then put a Hashemite -- that is, Sunni Arab -- ruler upon the throne of this creation, "Iraq." The British left, and the Arabs, having solemnly promised not to touch a hair on the head of the Christians, promptly started to kill about 100,000 Assyrians. The Sunni Arabs, who had watched the British suppress a result of the Shiite tribes, ruled, but there was not much to rule, and the instruments of repression of the modern state did not yet exist to enforce that rule in the way that the final Sunni Arab ruler, Saddam Hussein, so ruthlessly exploited. Saddam Hussein ruled for his own benefit, and that of his family and tribe, including many from his home town of Tikrit. But officially, the Ba'ath Party was open to all, and the odd Christian, such as Tariq Aziz (that was his islamized name), Kurd, and Shi'a Arab could participate, as long as they did not challenge the rule by Sunni Arabs camouflaged as Ba'athism.
The destruction of Saddam Hussein's regime made power flow from the Sunni Arabs to the Shi'a Arabs, who are three times as numerous, and who have no intention of ever relinguishing their own power, or even to sharing very much of it with the Sunni Arabs who, after all, lorded it over them, in every sense, for so long. And the Kurds, having tasted autonomy under American protection, are not about to go back to being ruled by the Arabs, Sunni or Shi'a, who brought them nothing but trouble and persecution and death.
So that's Iraq. Why should the American or any Western government want to keep Iraq together? It makes no sense. Let the Arab world descend into the Age of Warring States, or rather, not warring states, but wars-within-those--states. That will buy time for the Western world, and the rest of the non-Muslim world, to learn, to study, and to come to its senses about Islam.