Oh jesus.
Alright, there's obviously a distinct difference between Catalan and Spanish culture, and not nearly such a distinct difference between Phoenix and the broader United States. I'm not a sociologist, I can't provide you with a robust definition.
just fyi the definition of culture is one of the most hotly contended topics in sociology/geography academia and that you need to be really careful when you start using it as part of a definition
the ambiguities of territory size also applies to culture: at what point do cultures count as different? are the navajo same as the iroquois? is californian culture the same as rural kansas culture? what about the deep south vs the north, a la american civil war?
the fact is precedent shows that if a country wants to exist, it needs to defend its soverignity, and just letting anyone secede with a popular vote will cripple a nations ability to do anything. the US had to fight a war to become independent, and fight a war to keep itself together. even if society has changed you cant expect big things like secession and new statehood to just be resolvable with a democratic vote. just look at the state of politics in this country - its only over who has presidency, and yet it gets so violent and heated.