Zu "woman" sagt etymonline u.a.:
"adult female human," (...) alteration of wifman (plural wifmen) "woman, female servant" (8c.), a compound of wif "woman" (see wife) + man "human being" (in Old English used in reference to both sexes; see man (n.)).
It is notable that it was thought necessary to join wif, a neuter noun, representing a female person, to man, a masc. noun representing either a male or female person, to form a word denoting a female person exclusively. [Century Dictionary]
"man" in "woman" bedeutet also "Mensch", nicht "Mann".