I identify as an Arab because I am (last paragraph of this >>73530454
When I say "European culture" I am obviously speaking colloquially in broad terms. It's not meant to accurately represent all aspects of it. It's just an umbrella term that indicates those cultures that are similar to each other in the aspects relevant to the context.
Saying "Arab culture" would be equally appropriate if you're broadly speaking about the arab world, even if the countries that's made of have their own cultures, much like people say "American culture" even if its states (or even cities) have their own separate ones.
And you can go even deeper by saying "NYC culture is an offensive term" because NYC is made up of different boroughs with separate cultures of their own, but it's still absurd to consider it offensive because it doesn't "do justice" to its separate ones.
I honestly think it's a stupid and pedantic argument, and also it's very stupid to feel offended by the choice of words (or even the ignorance of a subject you're passionate about).
The only acceptable reason to get offended, IMO, is if someone is being malicious towards you. If someone is just using the incorrect words without meaning harm, and you still get offended, then you deserve to be offended.