Given the utter lack of clues, one can only speculate. However, one can't help but recognize here the parallel between Adam and Eve, and the Virgin Mary and Christ (not in the sense that I am the one who recognized it, but that it's impossible to ignore, and thus relevant).
Christ was taken from a single parent, his mother; Eve was taken from Adam, the first human in Creation.
When Eve was taken from the side of Adam, God closed up the flesh again. Christ took his humanity from the womb of Mary, but Mary remained a virgin. || ⚠️ Independent theologians may have called this matter differently ||
Adam and Eve were born pure, but everyone else afterward was born in sin. There was no helpmate found for Adam, for which reason one was taken from his side. Everyone before Christ and Mary were born in sin, and so Christ could not take up flesh from any old sinful mother, passing on the curse to Himself (the Saviour cannot have been Himself saved from the curse, so His mother must have been pure), so He made Mary pure from conception, and took flesh from her: the first of the New Creation. God made man, and then woman, but the devil targeted the woman to bring about the Fall: God undid this by starting with a new woman, and bringing the new Adam from her (cf. Gen 3:15). Satan went to Eve, Gabriel to Mary. Eve disobeyed; Mary: "Let it be done unto me according to thy word."
Standing by the tree of the knowledge of good and evil, Adam and Eve were there at the very moment of the Fall of mankind. Right then, Adam dubs his wife, the Woman, "Eve, for she was the mother of all the living." Whilst Christ hung on the tree of the cross, his mother stood by Him as He accomplished the Redemption, where he said, "Woman, behold thy son," to His mother, and to "the beloved disciple" (keep in mind the theological overtones to almost everything John writes...), "Behold thy mother." That is, to all the living in Christ - those of the New Creation ("The rest of her seed" after Christ Rev. 12).
This connection between Mary and Eve, Christ and Adam was not lost on early Christians. Irenaeus, an apostolic father, actually says that Luke intended the parallel of both.
All this to say that Genesis is a highly theological book of the Old Testament, similar to how John's Gospel is highly theological (recording events with language very given to theological understanding by its nature) - if we believe in the inspiration of both Testaments, we can glean information to help us understand both better. Why did God make woman from man? So that she could be truly Adam-ish (human), as opposed to something else: after all, no other helpmate was found suitable. But the entire narrative and way of doing things points forward to what God knows He is going to do - if not the events themselves, then how they are recorded for us, so that we can know and appreciate the foreknowledge of God.