The armed forces of the United States of America are to be used for one purpose and one purpose only - the defense of the United States of America and/or its citizens and interests abroad. Syria has not attacked the United States of America or any of its citizens or interests abroad (That I have heard of) thus, we have no business being there in any military capacity whatever. Those who feel strongly about "spreading freedom" to those who lack it may seek to move to those countries and join the armed forces of said countries for that purpose. For example, Israel's IDF has a division strictly for non-Jews/Israeli's who believe that protecting Israel is of paramount importance. I am sure other countries have similar accommodations.
If it is to become the purpose of our military to "spread democracy" around the globe and free the oppressed peoples of the world, then who do we attack next? When does it end? How many more of our men and women in the military must we lose or bring home minus limbs in our efforts to "save the world?" China has a long record of oppressing and abusing its people. Ask the folks in Tibet how the Chinese government treats people. Is China next on our list? How about North Korea? If not, then why not? How do we pick and choose? Why countries in the Middle East and not those in the Far East or elsewhere?