[V-2]

That might be true, but this is not as symmetrical as you're implying - in my opinion. There is simply more to know about Europe, since it's more diverse, has longer history etc. Also, the US happens to be a global superpower (and the only one nowadays) - no wonder it attracts more attention, and we're all naturally subjected to an influx of facts about it - the impact of its popular culture adding to it. It's, at least to an extent, of the same nature as the fact that we discuss in English now, regardless of what out first languages are.

A more balanced question than the one you suggested would be: does an average European know more about Europe than an average American about the US? :) That's closer competition here.

I lived in England for nearly 6 years and I wasn't exactly impressed by how much they know about continental Europe - let alone these parts of Europe that were on the other side of Iron Curtain.

And speaking of Americans, I'm sure that an average - say - Brazilian doesn't really have much of a clue about Europe either, despite Brazil's historical and cultural ties to Europe. Yet noone is talking about typical Brazilian ignorance and we'd forgive this without batting an eye. Why?

Because we usually know just as little about Brazil, so we are prompt to excuse them :) Not so in case of Americans (US citizens). It's the lack of symmetry that bugs people and provokes hostile reactions.