It's not the Bible itself that has a problem with women. True, it is a documentation of cultural history as well as a spiritual book, but I think it's the imperfect people of the world that decided women would be backseat drivers when it comes to God. It became so polarized that women were either seen as following the Virgin Mary as chaste, holy figures (even though Mary had sex after the Virgin birth) or as Eves, easily led, morally ambiguous risk takers out to tempt men.
So that's why I think the Bible has not been "updated." The underlying message of love and a relationship with God are timeless and so many parts of it are relevant today.