You seem to think Libya and Syria were all up to the American President alone. When in reality, he was only reacting to local developments there in an international context. Evidence points to the Europeans (French) being in the leading role for the bombings in Libya and Syria is a very convoluted area involving the Iranians and Saudis and on a second level the Turks, the Kurds, the Islamists, the Israeli, the Europeans and the Russians. The American President is an important player here, but it‘s not up to him alone to „start or finish the war“ there. That‘s Diplomacy for you.
The arming of the Free Syrian Army was done in cooperation with all Western forces. It‘s logical that the US contributes the most because they want to for reasons of their own Military-Industrial-complex. Being the capitalistic world dominator means you make sure that it is your own weapons that are used (and have to be bought). Just recently, the Americans forbid an Israeli company to sell a specific weapon to Switzerland (and I think Poland as well) to make sure that those militaries bought the US-american equivalent. I just want to show that the whole story is more complex than „the POTUS decides“. (Rant over)