What am I supposed to see here? (Are you, by any chance, be confusing the word "sexism" with the word "misogyny"?)

You're supposed to see that the media considers it to be malevolently sexist. Redefining the terminology so that "sexism" somehow is a neutral term is, for lack of a better phrase, "not an argument".

I don’t see it. I certainly see many references to it as a bad thing that needs addressing, just like germs are a real and serious problem that needs fighting, but that doesn’t mean that the people who spread germs do it with the intent to cause others harm. So I don’t see “malevolent sexism”, and I don’t see references to Damore as a misogynist.