(I) Illegality

Charter of the United Nations
signed by the U.S. president
ratified by U.S. Congress
supreme law of the land in the U.S. according to U.S. constitution

Article 2
The Organization and its Members, in pursuit of the Purposes stated in Article 1, shall act in accordance with the following Principles.

The Organization is based on the principle of the sovereign equality of all its Members.
All Members, in order to ensure to all of them the rights and benefits resulting from membership, shall fulfill in good faith the obligations assumed by them in accordance with the present Charter.
 All Members shall settle their international disputes by peaceful means in such a manner that international peace and security, and justice, are not endangered.
All Members shall refrain in their international relations from the threat or use of force against the territorial integrity or political independence of any state, or in any other manner inconsistent with the Purposes of the United Nations.
All Members shall give the United Nations every assistance in any action it takes in accordance with the present Charter, and shall refrain from giving assistance to any state against which the United Nations is taking preventive or enforcement action.
The Organization shall ensure that states which are not Members of the United Nations act in accordance with these Principles so far as may be necessary for the maintenance of international peace and security.
Nothing contained in the present Charter shall authorize the United Nations to intervene in matters which are essentially within the domestic jurisdiction of any state or shall require the Members to submit such matters to settlement under the present Charter; but this principle shall not prejudice the application of enforcement measures under Chapter Vll.
North Atlantic Treaty
signed by the U.S. president
ratified by U.S. Congress
supreme law of the land in the United States according to the U.S. constitution

Article 1

The Parties undertake, as set forth in the Charter of the United Nations, to settle any international dispute in which they may be involved by peaceful means in such a manner that international peace and security and justice are not endangered, and to refrain in their international relations from the threat or use of force in any manner inconsistent with the purposes of the United Nations.
Military action against is illegal so far because Syria does not attack another nation, is member of the UN itself and the UNSC did not give green light.
Granted, a specific law of the U.S. Congress weighs heavier than a less specific one, so a U.S. law permitting an attack on Syria weighs heavier than the less specific UN Charter and North Atlantic Treaty. An attack would still be an illegal act and violation of both charter and treaty if looked at by other member countries, of course.
An attack of Syria would basically be a violation of the duties as a NATO member. But that's nothing new to some members, of course.

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(II) Illegitimacy

Legitimacy (UN aside) can only be had if the action is a ceteris paribus improvement. It cannot be legitimate if it makes the crisis worse.

Killing and destruction is clearly bad in itself, and requires to be outweighed by benefits.
No such benefits have been laid out convincingly.
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(III) Efficiency

If civilian suffering is the issue, why not help civilians? Why add destruction, instead of humanitarian goods, to the mix? Compare the cost efficiency.
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(IV) ...


(More than enough arguments already in my opinion, so I'm not motivated to sum up all the others. Feel free to add them.
This thread was created because I disliked the imbalance of having a "case for action" thread, but no "case for inaction" thread. The urge "to do something" is strong in humans, but this doesn't mean that action is better than inaction - especially when one can avoid involvement.)