Duty, their rearholes. They're accepting so many refugees because they have to, or else the entitlements Europeans currently enjoy will dry up, and they'll all be working till they croak because their native populations aren't popping out enough babies to keep the system going in perpetuity.
As I see it, Europe has faced six primary existential crises to date, crises that fundamentally shaped the identity and future of Europe:
1. France, 8th Century AD and the confrontation between Martel and the Ummayyads that saw the eventual rejection of Islam in Europe
2. The repelling of Asiatic invaders (namely the Mongols and Tatars) from the European center
3. The Thirty Years' War and the Peace of Westphalia
4. The defeat of the Ottoman incursion into the European heartland in Vienna
5. The defeat of fascism
6. The defeat of communism
Europe's population crisis and the almost necessary influx of cultural "outsiders," pitting Europe between a rock and a hard place, is now the seventh. Whether or not it comes out ahead in this one, I do not know, as it is a much more perfidious crisis that cannot necessarily be met head on with force.