The supposed strength of "the family" comes from specialization of roles. Specialization means learning to do something really well and practicing it with dedication, at the expense of not doing and learning anything else. In the nuclear family model, the man is specialized in working to provide for the family, while the woman, is specialized in producing and taking care of the children.
What is not directly obvious is that bringing in resources and being a provider is a much more powerful position or status, and inherently takes away power from women who are relegated to acting as house slaves with no other significant purpose other than reproduction. To put it simply, there's much more power in being a producer, trader or worker instead of being a stay-at-home baby-making machine that always depends on someone else to bring resources.
And if people accept this model, other consequence are that women do not need education, beside general education and "home-skills"; women have no place in the working environment where men work; and obviously women can't hold positions of power like teaching or leading in politics; and why should they vote if they're not really educated and out and about in the World?