Also, I can pretty much guarantee that even if someone slipped through the cracks and committed an act of terrorism, the number of people killed as a result would almost certainly be less than the number of refugees who will die from us closing our doors to them - and yes, American lives and Syrian lives are of the same value.
The thing is, the American government exists to serve the interests of the former, not the latter. If even one American life is imperilled by refugee resettlement, it should be off the table.
1.) Whether we like it or not, we have made ourselves leader of the free world. We have taken on responsibilities beyond the lives of Americans, and our foreign policy has reflected that. I mean think about it, when we hear about violence in Ukraine, Syria, etc. the conversation in the U.S. is 'how are we going to fix this?'. We have made ourselves responsible for what happens in the world. If you don't want that responsibility, then maybe you should adopt an isolationist foreign policy.
2.) We are in many ways responsible for what has happened in Syria, through our invasion of Iraq and premature withdrawal. It would be highly irresponsible of us to shirk our responsibility in this situation.