And yet, in the OT, he chose a woman - Deborah - to be judge over the nation and leader of men.
There is certainly something to say for a handful of women in scripture like Deborah or Priscilla or the prophetesses, but I think you have to take each scenario independently and look at the context.
In the case of Deborah, I see it as one of the exceptions to the ideal. If you think about it, God didn't really want any judges (male or female), like He didn't want kings. God always wanted His children to be directed by Him. Exceptions were granted, especially in the pre-Torah period--for instance, incest was acceptable at some points, even though later that became an abomination. There was the exception, but only for a time. Maybe the exception in the case of Deborah was because the male Judges were failing over and over...the people were failing over and over, drifting from God, doing "what was right in their own eyes".
But I don't think it's a coincidence that God chose Abraham, Noah, David, John the Baptist, etc., and especially Jesus, as well as the apostles--being males. Between the curse given in Genesis, and Paul's teachings about headship/women's
quietness/inability to teach over males in the congregation, it's clear that the Man is to be the head of the household in the family and to take the responsibility to teach and guide in the location congregation of Christ (hence also why elders and deacons are to be men only).
That's the biblical way. It's God's way. It's not a societal matter for that time, it's an institution from the beginning that God expects us to carry out until the end of time. At that point men and women will truly be in the exact same position since we will no longer have flesh..we'll all just be spirit at that time (hence why Paul says "in Christ there is neither male nor female"). But while we are living in flesh, we must abide in the institutions of God.
But I repeat, women are not inferior, just different. And they must be appreciated, honored, respected, loved, and cared for deeply...both in the marriage home and in the local congregation for their roles.