One significant thing that you are missing is a sense of making good on past misdeeds. Europe owes it's economic power to centuries of fucking over Africa, the Middle East, and Asia. And when they de-colonised those places, they set up systems to keep them fucked up. So when you see refugees trying to escape those places, there is a sense of duty to them.
A clear case of this is Syria, which is in the shitter because of the Western destruction of Iraq fifteen years ago. Before the US went in, a number of critics were saying that the US had no exit plan and that removing Hussein would massively destabilise the region - both turned out to be true. So when millions of refugees stream out of there, "our side did that to them".
Another thing you're missing is that Europe still has in living memory the scars of what happens when you're divided rather than unified. We don't have the pain of nazi occupation and collaboration here in Anglotown. WWII had not only country against country, but neighbour against neighbour, and we Anglos have absolutely no idea of what that was like. The same thing happened more recently in '90s former Yugoslavia. European unity is about more than free trade.