As the previous posters have stated, it's complicated.

If Assad's regime falls, the Al-Queda and ISIS affiliated groups move in. I'm not sure America wants that. Do we want that? Hard to say!

Saudi Arabia supports the Assad regime falling because the Assad regime is not Sunni.

If we set up a no fly zone in Syria, we are then in direct conflict with Russia's forces. It's no longer a proxy war.

I hope there's a way to be against US intervention in Syria(if only because of grim realpolitik reasons) and simultaneously not defend Assad.

I fully recognize that the Assad regime is terrible(I can pummel you with New Yorker articles). I don't quite believe the Assad people used poison gas, I think the jury is still out on that.