Commenters may want a Syria thread.
I have no peculiar insight to share with you, only the commonplaces.
Obama´s arguments for intervention:
P1. The use of poison gas is a war crime; against civilians, an odious one. It should be punished if possible.
P2. He, Obama, personally laid down a red line on the subject. Failure to follow through weakens the standing and credibility of the US.
P3. An intervention limited to bombing is likely to greatly reduce the Syrian government´s capacity and willingness to use chemical weapons again in the civil war.
A1. A unilateral armed intervention, however limited, without the sanction of the UNSC, is itself a violation of international law. There is no prospect of an UNSC resolution authorising force, given Russian and Chinese opposition. You can´t uphold international law by means that violate it. (UNSC sanction isn´t needed for self-defence, but nobody is claiming that this applies.)
A2. The intervention has no prospect of ending the conflict through bringing about a negotiated peace, or the victory of either side.
A3. The slippery slope: given the very limited effect of the bombing envisaged, it will create strong pressures for further and more decisive involvement. This would have unpredictable outcomes, many of the possibilities being very bad.
A4. Precedents: the recent history of US armed involvements in the region does not support optimism about the effects of another one.
A5. Credibility does not require you to make good on all your threats, which makes bluffing unusable. It´s unlikely, after Iraq 1 and 2, Afgahanistan, Bin Laden, Guantanamo, Kosovo and Libya that foreign rulers will suddenly stop worrying about threats from the US government, especially on matters where its national interests are more clearly at stake.
Am I leaving anything vital out?
FWIW, I give a lot of weight to A2. The interventions in Kosovo and Libya were also illegal by the same standard, but they had the merit of being decisive. The standard criteria for just war include a good chance of winning; you should not shed blood for symbols.
In the Libyan case, it´s actually a good thing that Obama, Cameron and Sarkozy lied about their objectives of the bombing: their real aim was to overthrow Gaddafi by backing his opponents (a far more united and credible bunch than the Syrian rebels), and their means were sufficient to achieve this. Libya is still a mess, though probably an improvement on Gafafi´s creepy police state.