If you write about rapists it needs no qualifier. If you write about men, all men is implicit unless you qualify it with the subset of men you are writing about.
It is a huge problem today that people draw their circles much too large as if they never learned set theory in school. I’d call it an improvement if “not all men” was replaced with, “be specific, which men?” though I agree with you that it would be great if it went away.
Would there have been something wrong with replacing the “Why are men today taking everything so personally?” that you wrote with “Why are some men today taking everything so personally?”
I give you the benefit of doubt that you meant some men, but an explicit some men would most likely put an end to “not all men” or greatly reduce it. Leaving the qualifier out almost seems like bait.