It's about believing you're the seat of culture on the entire planet - even if more people spend money on Hollywood, they just don't do slow B&W films about peasant women during WWI poignantly losing their virginity anything like as well.
It's about believing that being nice and getting along with most people is better than exploding them into small pieces and raping their women. (And/or men.)
It's about real style and class and poise, instead of the pretend style and class and poise that having money but no taste gives you.
It's about ideals rather than realities - some of which are plausible, some of which are silly, but all of which hide under a very quiet fervour that the rest of the world hasn't realised is there yet.
I think Europe is in danger of believing its own propaganda. (Much like the US does.) We'd like to believe we're nicer and more civilised and that we own the moral high ground, especially wrt the rest of the world. But the reality may not be quite so simple.
Still, Europe is better than a lack of Europe. Imagine Europe without any Europe at all. It just wouldn't be the same, would it?