Historically, "man" comes from Old English "mann," which originally meant "human being" or "person" in a gender-neutral way, without specifying male or female. Back then, the word for a male human was actually "wer" (like in "werewolf"), and for female, it was "wif" (as in "wife"). Over time, "man" shifted to primarily mean "male," but terms like "mankind" hung onto that older, inclusive sense.
So, using "man" in the "mankind" context isn't really a misuse or inherently sexist: it's tapping into the word's original roots. That said, I get why folks prefer "male" and "female" for clarity today. Peace!