It's NOT BS. Sixteen+ years I've faced that bias; it's real, it exists whether you want to admit it or not. In fact, I got into a discussion just this last Tuesday on a NON-divorce forum that I belong to; specifically, the subject was that there MUST be something "wrong" with a Mom is she doesn't have or want "custody" of HER children...it's not "natural".
Mind you "shard" custody is "ok", but for Mom to be the NON-custodial parent...even in our so-called enlightened society where homsexuality, multiple mothers/fathers, "domestic partnerships" have become a normal and acceptable practice...a female NCP is still NOT accepted.
As for the possessiveness...unfortunately, I don't that that will ever change since men can't gestate and give birth.