They're like states, if the states each spoke their own separate languages and had spent the bigger part of the last 2,000 years constantly at war with each other.

I'll explain. People get annoyed because you are proudly ignorant of 2000 years of history and tons of cultural differences.

I mean most American states are shaped as rectangles, have nothing notable in terms of geography or culture to tell them apart, and are under 2 million inhabitants.

It's like if Europe had Estonia, Latvia, Lithuania and then 15 more of that, but they're all shaped the same and speak the same language and their capitals are made of cinder block and plaster.

Appreciate the warning! I think the real problem is that Europeans never accepted they are becoming a single political entity and still don't necessarily consider themselves European. I think that's sad, as Europeans are extensively closer to each other than to nations outside of Europe. Also, the EU is a decent model for how smaller entities can work with larger ones without being suffocated or absorbed.

Europeans think of any European country as an equivalent to America as a whole.

Half of the problem with that phrase is that this line of thought is far more common from Americans than Europeans. No European think France = US in any other context than geopolitically, maybe. But a lot of US citizens do think that way. The phrase “Americans think 200 years is a long time, and Europeans think 200km is a long distance” is of US origin. It's literally the result of US ignorance that compares the geographical distances of a single European state, like Germany or France, to the entire extent of the continental US. Europeans are perfectly aware that 200km are 200km anywhere on the planet. Whether you are driving to another country or another state, it is irrelevant.

The other half of the problem is that the political dynamics of the European Union are fundamentally different to the United States federation. Just by the fact that the US was forged in war while the EU is an economics first agreement. Their nature is vastly different and not comparable at all. Maybe one day in the future the EU will just be a federation of states, a single country with a single constitution, but today that's not the case. There's no executive power in the EU that can override a country's authority. That alone sets them so very far apart.