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especially since many such words are probably older than the current use of "man" to mean male person, and refer to the older sense of person, as in the US constitutionI feel like that use is... complicated. Why, exactly, did "man" mean "person"? Why not "woman", then? It feels like using "man" to mean "person" -- including and especially in historic usage -- is itself patriarchal. Given the time period you reference -- the writing of the US Constitution -- I think it's even more stark, as it was written by men who were not inclined to allow women any sort of participation in the government (and I expect many of them did not feel that women were as entitled to many of the rights they were enumerating).
But really, the semantics aren't the primary issue. If a lot of women feel excluded by "man"-terms, then that's a problem. To be fair, though, I have never asked a female police officer or firefighter if she felt that "policeman" or "fireman" made her feel excluded, so I don't really know.
I think "excluded" is a better term than "offended" in some cases. "Offended" is a very squishy, subjective, imprecise, emotional term. What matters is why someone might feel offended by a particular term, and I could certainly sympathize with a woman who felt like "policeman" was implicitly telling her that she wasn't fit for the job, that women should be excluded from consideration for that job, or that women should intentionally exclude themselves from considering wanting that job.
As much as I disagree with a lot of the things on Stanford's list, I think calling words "harmful" is better and more descriptive than calling them "offensive".