It's interesting being in Europe or somewhere and having a bunch of travelers introduce themselves, I've always noticed that most people will say what country their from, Italy, France, Canada etc, but Americans always just use their state.
Interesting topic. In Europe it seems by country. From France vs from Paris
For example if you're in a German train and ask someone where they're from, they might say they are from Swabia (a linguistic region similar but not identical to the state of Baden-Württemberg). If you had asked them in a Swabian accent, they would have instead answered with the specific city, e.g. Limburg. If you ask the same person in English while he's on vacation in Paris, he'll say he's from Germany.
What people actually identify with most strongly depends heavily on the region; in large cities it's often the city or metropolitan area, but elsewhere it's not uncommon to associate with linguistic regions, kingdoms that stopped existing centuries ago, or your state or administrative district (particularly when it coincides with one of the previous points).
Saying your state is imo closer to saying your European country instead of saying Europe.
Additionally, culture and education being what they are, most adults in western countries have heard of all the states, moreso than some of their principal cities, so it's not that odd to mention it.