A better question is why Hillary Clinton and other state and defense department personnel think he will quit and leave Libya.
After all, Libya is a paragon of multiculturalism and diversity, the model of statecraft the U.S. is pursuing in Iraq, Afghanistan, and elsewhere around the globe based on doctrines taught in American universities.
Too bad that Libya is a tribal society and that those supporting Qaddafi have cause to fear for their lives and welfare should rivals in Benghazi and elsewhere come to power. Think in terms of Shia versus Sunni in Bahrain, Saudi Arabia, Iraq, Yemen, and Iran. Qaddafi and his family are not alone in clinging to power. It’s also his own tribe and southern Saharan tribes from Libya’s old southern desert province of Fazzan and others that have tied their masts to his.
At least, so far, Hillary has had the good sense not to take on Syria’s Assad in the quest to build a multicultural democracy in that nation.