From his own mouth

"Trying to eliminate Saddam, extending the ground war into an occupation of Iraq, would have violated our guideline about not changing objectives in midstream, engaging in "mission creep," and would have incurred incalculable human and political costs. Apprehending him was probably impossible. We had been unable to find Noriega in Panama, which we knew intimately. We would have been forced to occupy Baghdad and, in effect, rule Iraq. The coalition would instantly have collapsed, the Arabs deserting it in anger and other allies pulling out as out as well. Under those circumstances, there was no viable "exit strategy" we could see, violating another of our principles. Furthermore, we had been self-consciously trying to set a pattern for handling aggression in the post-Cold War world. Going in and occupying Iraq, thus unilaterally exceeding the United Nations' mandate, would have destroyed the precedent of international response to aggression that we hoped to establish. Had we gone the invasion route, the United States could conceivably still be an occupying power in a bitterly hostile land."

Brent Scowcroft and George H. W. Bush's A World Transformed (1998).