In those contexts historically "man" = "human being", rather than "male human being" The same way "dog" = "canine being" as well as "male canine being". (It works the other way round for goose and gander.)

It's a quirk of the language. In that context the romans would have used "homo" (human being) rather than "vir" (male human being) - and that didn't in any way imply that Romans were not extremely sexist.