> If treating a large group as a unified actor is improper, then giving another group another label and doing the same thing...because it's that group is in a different classification, is also improper.

I think this is the logical leap that people aren't understanding. Generalizing means assuming things about individuals based on their group membership: OP wasn't saying it's a moral failing, but that it leads to inaccurate assumptions when applied to the heterogenous group in question.

What's the analogy to using the term "the masses"?