1. I have no sympathy for Assad who would probably deserve to be hanged in the best of the worlds. However, we do not live in the best of the worlds. We live in the real world, and in this world there is Al Qaida. In Syria it is called Front Al-Nusra. If Assad is overthrown these guys will take over (moderate opposition perished in the civil war long ago), slaughtering Alaouites, Christians (Are the American conservatives really going to vote for that?), dissenting Muslims... From this point of view, the evil Assad is the lesser evil.
2. What would be the purpose of a hypothetical bombing campaign? Some say the use of chemical weapons (just assume Assad used it, no proof has been provided, but never mind - our governments would not lie to us, would they..?) should not go unpunished so that other dictators would not be tempted to follow Assad's example. However, just throwing few bombs on Syria would do little damage to the regime, the equilibrium of forces on the ground would be unchanged. But then it would not provide an adequate disincentive neither to Assad nor to the others. What do they lose by using WMD, a couple of tanks?
3. To provide an eficient deterrence the intervention should cause serious damage to the regime (e.g. wipe out the Syrian army; eliminate Assad). But then, the equilibrium in the civil war would shift to the benefit of the rebels and we are back to my point 1.
4. To avoid an islamist takeover, the American and the Europeans would have to step in, put a puppet government, inject dozens billions of dollars/euros, suffer losses from guerilla... Wait a second... this solution just failed in Afghanistan.
5. And then, there is a financial element in it. The socialist government in France is imposing painful cuts in pensions and public expenditures, but stands ready to finance its bombing campaign in Syria. Are those who had voted Hollande fine with that? (Of course I am talking about ordinary people, not Bernard-Henri Lévy)
6. Democracy, regime change are good objectives ! Why not start by Saudi Arabia, Qatar, Bahrein (where the popular uprising has been suppressed manu militari without a word of protest from the western democracies)?
7. There should be a political solution involving all the sides. Two conditii sine qua non: Assad family steps down, Al-Nusra is wiped from the face of the earth.