From the Ink Spots blog comes this, as good a statement as I've seen of why we should not intervene militarily in Syria:

I am with Dr. Slaughter in her disgust for the Syrian regime for what they are doing to their own people. I agree that they have violated their responsibilities as leaders. But I hesitate to support the use American military force to wage war in an action that is likely to result in the deaths of more civilians than the regime's current actions. Values are an American interest, but are they worth war without overwhelming support from the rest of the globe? I don't think so. Values are a great reason to flex the United States' ample diplomatic and economic capabilities as this approach is more in line with our values.

Tom again: Also, once we intervene, I think we are in part responsible for subsequent events. What if the eventual winner in Syria starts driving out or killing minority groups? Do we intervene again?