Iraq has always been the hub of the Middle Eastern country politics. The reason to stay in Iraq is quite easy to decipher. Not only it is important strategically from a nuclear point of view but also its stability means a lot to the peace of the world overall.
As we are aware that when Iraq was engaged in a fierce battle with Iran (for about ten years on an average), the President Saddam Hussein had all the funds of the country directed to the development of the defense arsenal. He and his sons not only amassed billions via selling of oil to the world, but also started stockpiling weapons of mass destruction. This was the main reason behind the United States of America declaring war on Iraq. Even after the war was over, there were reports of political instability which was a good enough reason to stay in Iraq till the new regime started functioning well.
Another good reason to stay in Iraq was the weak Saudi Arabia where retraction of troops would have meant some another form of retaliation by the hidden anti social Iraqi elements. Saudi Arabia shall always be a high target on the elimination list of religious fundamentalists. This is because it allowed the US President Bush to set up his base on the soil exposing all the strategic defense locations of Iraq for the missile attacks that weakened and exposed the strong defense of Iraq to the American missile attack during the war.
After the capture of Saddam Hussein, people thought all over the world that finally the terror was over. But the threat is very much the same and this is a big reason to stay in Iraq to monitor the movement of the rebel Iraqis who are getting safe passage in other countries. Only the focus has shifted to the Asian countries predominantly. These countries include the friendly fundamentalist forces of religious bigotry encompassing the likes of Afghanistan (Osama Bin Laden still hiding after 24/7), Pakistan (monetary funding and training camps for the brain washed youth to result in a never drying stream of terrorism), Sri Lanka (safe haven and financial aid to rogue countries and terrorist activities in the Middle East in exchange for arms and nuclear capability).
The crucial bombing of the twin towers of the World Trade center and Pentagon in quick succession has served a lesson to the United States that reason to stay in Iraq becomes all the more important as a part of the long term strategy to weed out the terror big time. The threat of the suicide bombers planning calculated revenge attacks shall be lessened if there is an effective deployment of the US troops in the important areas. Not only this may allow the UN inspectors to effectively unearth the links (which can only happen when the troops engage in spying activities big time with the local police) but also give Iraqi people a much needed hope of peace and calm.