Well, there's a few distinctions to be made:
Refugee status is one thing.
"Wanting" to move to the US legally is another thing.
"Wanting" to move to the US illegally,yet another.
To that end, don't get to mericacentric about this: they aren't packing up the bombed out apartment building and kids and getting on boat to Europe...
...cuz they "want" to go to the US. They simply have run out of options,and europe, traditionally has had two things going for it:
Established muslim populations and therefore potential of actual relatives/family up there
The US has some muslim populations, but look at how they're being treated now. Quickest way to radicalize someone anywhere? Make their life and quality of life feel worthless and hopeless...and 66 virgins in heaven looks pretty flash. And to be fair, in the US with the lack of mental illness priorities and such, we see the same sentiment by these young lone wolf males who feel "useless" and take it out on folks in movie theatres,schools,etc.
And we apparently like winless wars over tolerance now...
The fact is most of this Syria shit started around 2006, when the combo of Iraq refugees (oh the irony),lots of them farmers, went to Syria as the US invasion destabilized or blew up their lives in Iraq. At the same time, a monster drought hit Syria and crops collapsed, which caused rural farming Syrians who were poor as fuck anyways, into the same areas of Syria where the Iraq refugees went.
Strains on society ensued; rival existing factions took advantage of the situation, and a dictator felt his stability rocked, started bombing his own country to restore his power platform.
As more and more of the world suffers droughts, floods, sea level rise,etc. You will see more refugees....and not from the middle east,and not just from religous wars or US war profiteering. From what I read recently, we're looking at 100 million refugees worldwide being checker pieces by 2030 due mostly to climate related issues; which have a knock on effect as described above.
It's gonna be ugly, no way around it. But the moving to the US of all places is not the dream or #1 desire of most refugees in the M.E. Pomy English teachers? Sure....and they should be let in. But you have to ask in those instances, is the US immigration dept keeping some foreigners who WANT to move to the US in order to protect job opps for folks actually born here and are citizens? Does that not make sense to most; left or right leaning? NZ does not let folks move here and take jobs that kiwis could do; they accept skilled migrants that fit particular shortages in their industries. But we also take in refugees....cuz kiwis are tolerant like that. Last April, I took a cab to a rugby match; a paki driver on the way in, an afghani on the way out. Nice folks, sad stories about them getting in, but their parents, families still there in strife. Got back to VT,and no kidding, got a cab from the airport, and Iraqi refugee. Ex-translator; would've been killed if left in Iraq. Whole family still there. Asked him if he was treated ok in VT, he said, mostly,yes. But tough situations all around, no doubt about it.
I see Peetso put it succinctly...