I mean, one of the more quoted lines in LOTR is a human woman telling the Nazgul Witch King “I am no … man.” The film quote is shorter and more direct but the book still has Eowyn telling the witch kind she isn’t a man. So there are men and women but also man is used to describe humans.
This feels like one of those European translated turns of phrase. Like in Dutch there is a phrase that translates to “monkey sandwich story” that is used to call somebody a liar.