The more difficult question is what happens after Assad is defeated. One lesson that the United States learned in Iraq: It's difficult to keep armed adversaries from killing each other. Tamping down Iraq's sectarian violence required a massive commitment of ground troops over several years, but it's not clear that the mission succeeded.
Who is better for the United States, Assad or the rebels?
Neither is good for American interests. Assad, in addition to being an oppressive dictator at home, is an anti-American leader who supports Iran and the Lebanese militant group Hezbollah. But at least he had been predictable.
There's a growing fear that the rebels could be worse. Some groups say they want democracy, but some openly espouse allegiance to al-Qaida and are already imposing a severe form of ultraconservative Islamist rule in areas they control. It's not clear who would come out on top, but political vacuums tend to empower extremists.
The United States has already seen this movie in Afghanistan, where after an amalgam of rebel groups forced out the Soviet-backed puppet government, infighting among them led to civil war and ultimately Taliban rule. Perversely, the best way to keep this from happening in Syria is for the Assad government to retain at least some power.
How would strikes affect U.S. relations with the Arab world?
It sure wouldn't help. Although some Arab governments support strikes, Arab people tend to be deeply uncomfortable with the idea of Western military intervention in their region.
The first Gulf War, in which a U.S.-led force expelled Iraqi troops from Kuwait in 1990 and 1991, inspired pro-Saddam Hussein protests across much of the Arab world, even though Saddam Hussein was not particularly beloved. And the scars of the U.S.-led 2003 invasion of Iraq have not healed. U.S. strikes on another Arab country, even if meant to ameliorate the war, are not going to help America's already-troubled image in the region.
How would strikes affect U.S. relations with Russia and Iran?
If you support confrontational approaches to Russia and Iran, Syria's two main allies, airstrikes on Syria probably make some sense to you. Crippling Assad would weaken them, too, and send a message to Iran that the United States is willing to use force to deter the use of chemical weapons.