Yes, there's no way to say either of those statements to a member of a given group and not offend that person.

I can understand this. But things can be offensive and still be true. It's a possibility. I'm not particularly fond of pointing out, or even researching, possible differences between groups of people; however, the insistence on the opposite, when it's not perceived as backed up by substantial proofs, ends up provoking a response from those who value truth at least as much as harmony.