Obama hasn't intervened in Syria for the same reason he hasn't bombed Iran. He's really not into military action, except for aspects he can't avoid without looking weak (which is why the drone strikes just keep on coming). I think he should have just bombed Iran. A nukeless Iran will deprive the Gulf kingdoms of any excuse to have their own nukes.
Obama is a globalist. He went to war with Libya because the UN said so. He’s not doing anything about Syria because the UN didn’t tell him to. It’s that simple. Obama will do whatever the UN says, and he will not do anything they do not tell him to do. Period.