Interventionists. Those supporting the president's apparent proposal for limited strikes to "degrade" or deter Syria's ability to use chemical weapons against its own people believe that such behavior—the indiscriminate slaughter of civilians (including children)—cannot be left unpunished. The United States has a moral obligation to enforce international standards, as well as support allies in the region more directly affected by the conflict. If we don't act, American credibility will be compromised.
Non-interventionists. The slaughter in Syria is horrific, but our ability to impact an internal Syrian matter is limited. A limited bombing campaign is so incapable of solving the problem, that even its boosters talk only of "sending a message". And if the message is "kill all the people you want, just not with chemical weapons," what happens if and when Assad gasses his own people again? Finally, engaging in the war on the side of rebels dominated by Islamists worked out not-so-well in Afghanistan. What makes anyone think things will be different this time?