The schism between Shia and Sunni Muslims goes back to the early days of Islam, when the death of Mohammed triggered conflict over the identity of his rightful successor. While the schism runs deep, and is present in fighting in Pakistan, Saudi Arabia, and Bahrain, in addition to Iraq, the influence of the Iranian Revolution of 1979 fundamentally and radically altered the dynamics in the relationship between the two sides. Despite the Persian -- as opposed to Arab -- ethnicity of the Iranian clerics who assumed power after the fall of the Shah, Shia Islam now had a major, and powerful, benefactor to match the wealth and political influence of the Sunnis, who globally outnumber Shiites and provide the majority populations of major Islamic countries like Saudi Arabia, Egypt, Indonesia, and Malaysia.
Saddam Hussein's iron rule over Iraq, a majority Shiite country politically dominated by Sunnis, was justified by his claim to be the bulwark against the spread of Shia influence after the Iranian Revolution, as well as by his anti-Israel posturing and support for anti-Israel terrorist groups. Saddam's policies were highly discriminatory against the Shia, and, when the United States launched Operation Desert Storm in 1991 to evict Iraqi forces from Kuwait, Iraq's Shiites revolted against his brutal rule. After Desert Storm operations were halted, with Saddam's regime still in power, the Iraqi Army and security services were unleashed against the Shiites who, unlike the Kurds in the north, did not enjoy the protection of the U.S. military. Thousands of Iraqi Shiites were massacred, and the marshes that provided the historical home for many of these Shiites were drained to deny them their livelihoods and cultures.
When the Administration of President George W. Bush launched Operation Iraqi Freedom in 2003 with the goal of removing Saddam's regime from power, the country's Shiites were free to begin their fight for political power. The combined actions of the emergent Al Qaeda in the Mesopotamia terrorist organization, a militant Sunni movement, and the Mahdi Army of virulently anti-U.S. Shiite cleric Moqtada al-Sadr combined to ensure that Iraq would slide toward a civil war from which it has not and may never recover.
There is no doubt that the U.S. Government (with some dissenters) drastically underestimated the political fragility of Iraq and the extent to which Saddam Hussein's brutal rule kept a lid on the sectarian fighting that has raged since his fall.
A possible thesis statement, therefore, could read something like this: the U.S. invasion of Iraq ignited a conflict between Islamic sects that has destabilized the entire Middle East.