Taking in refugees over here is actually economic warfare against ISIS over there.

[DetlefK]

http://fortune.com/2015/09/27/isis-money-problem/
http://www.cracked.com/blog/isis-wants-us-to-invade-7-facts-revealed-by-their-magazine_p2/

ISIS is essentially an occupying army, not a state. It has no national identity, because huge parts of the population don't agree with ISIS.
But just like a real nation ISIS needs money. ISIS needs a budget, ISIS has a war to run, ISIS has weapons to buy, ISIS has fighters to pay.

But where does ISIS get this money from? First there was bank-robbery, but now there are no more banks to rob. Now ISIS gets the money for its budget from (among others like selling archaeological artifacts and oil on the black market) taxing the population.
ISIS made $1.2 billion in 2014. Out of those, $100 million were from selling crude on the black market. It is estimated that ISIS made several hundred million dollars with taxes.
Iraq has stopped paying government-employees in ISIS-territory so their salary won't fall into the hands of ISIS.

What do the refugees have to do with that?

Every refugee that makes it out of ISIS-territory is one worker less in their economy.
Every refugee that makes it out of ISIS-territory is one taxpayer less in their state.
Every refugee that makes it out of ISIS-territory is one potential recruit less in their military.
Every skilled worker that makes it out of ISIS-territory is another nail in the coffin of the economy and infrastructure of ISIS.

ISIS is currently waging a propaganda-campaign (with rich cornfields, bustling markets and busy city-streets, none of which are real) to keep people from leaving their territory.
http://www.express.co.uk/news/world/605911/Islamic-State-ISIS-video-Syrian-refugees-Europe-caliphate



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You want to hurt ISIS?
Steal their population.