I honestly respect the interventionist position and I agree that there are honorable reasons to support a military intervention. Nevertheless, I disagree with it. First off, as the video you posted makes clear, it's not at all clear what;s going on. Without having a much better picture from the UN inspector guys then I'm not confident to form a firm opinion of my own. Do I think that the Syrian government might use chemical weapons? Sure. Can I say with reasonable certainty that they have? No.
The fog of war that surrounds this chemical weapons issue serves to highlight the high level of confusion on Syria at the moment. As other posters have commented, there are multiple competing factions and some of them are pretty unpleasant. It's difficult to imagine a suitably well defined mission for a limited intervention that would make things better and allow the UN / NATO / whoever to withdraw in good order in a timely fashion.
Added to this is the problem that Syria's air defenses, while not state of the art, pose a non trivial threat to western aircraft. Either we stand off and lob cruise missiles or we put in a lot of work suppressing these defenses. Neither of these options is appealing to me. I'm from the UK, and I appreciate the legitimately strong desire to avoid another WTC type attack. For all of that, I'm tired of having my friends sent off to sandy places to get shot at and blown up in military operations that have achieved little
People say that they want to stop any country becoming a base for terrorists. Fair enough. That's why we went to Afghanistan. The problem is that after a nasty and protracted struggle we're just going to hand the place back to the Taliban. I'm not exactly a pacifist but I'm sick of throwing troops onto complex and morally challenging battlefields where they can get killed for little gain. For all of their sacrifice can we honestly say that we've made the world a less shitty place?
I feel bad for people suffering under brutal regimes, but as a citizen of a democratic country I feel more responsibility for the guys who are supposedly executing the will of the people as expressed though ballot boxes in the west.