One wonders if the Neanderthals were the inspiration for the "Nephilim" of Genesis 6:4:
The Nephilim were on the earth in those days-and also afterward-when the sons of God went to the daughters of men and had children by them. They were the heroes of old, men of renown.
I have often wondered the same myself. If Y chromosome DNA shows some Neanderthal genes then it would support this hypothesis. THeir men took our women, but we did not take theirs.