The Clinton Doctrine was not "the US will intervene in any case of atrocities against civilians"

[Recursion]

The Clinton Doctrine was that the US will intervene in civil wars if and when that intervention advances US and international security. (This was in a long-ago time when US and international security concerns were considered largely consonant.)

The actual quote that laid out the doctrine is this:

The true measure of our interests lies not in how small or distant these places are, or in whether we have trouble pronouncing their names. The question we must ask is, what are the consequences to our security of letting conflicts fester and spread. We cannot, indeed, we should not, do everything or be everywhere. But where our values and our interests are at stake, and where we can make a difference, we must be prepared to do so.

When you're the regional hegemon, inaction is a form of action; the opposite of "arming the rebels" is not "doing nothing", but "embargoing the rebels".

If you are convinced your preferred solution to the situation in Syria is obviously and manifestly the right one, I respectfully suggest that you need to study this more. No option here is very good at all.