They do! Germany, the UK and the Scandinavian nations are the only European countries (that I was aware of circa within the week) to be actively accepting Syrian refugees - every other country in between them AND the Mediterranean have had negative responses to incoming refugees and I would expect deportation.

If refugees were just coming in for safety's sake, there are plenty of other Islamic countries that would be more culturally compatible (that argument would fail in the case of Syrian Christians; I don't know the full proportion of real religious denomination to refugee count). There are plenty of European countries that want no business with refugees, like Hungary, who have just declared martial law in the last few days or so wrt refugees.

It's a choice. It's a hard choice, one which tangles several levels of liberal beliefs of tolerance in a democratic state and respecting a country's historical/ethnic heritage, which is why I think there is so much controversy. I personally don't see how any country in Europe is obliged to accept refugees.