The entire Bible - the inspired word of God - gives example after example of men He selected to lead His people in every institution He brought into existence. Adam, Noah, Abraham, Issac, Jacob, Joseph, Mosses, David, Solomon, Job, Isaiah, Jeremiah, Ezekiel, Daniel, all the Apostles - all the historical leaders of the people - were males. Even the pagans were lead and ruled by men. The few women exceptions were just that - exceptions by unique cause. Was God a sexist because of this? No, He was merely following His own design for man and woman which He instituted at the creation. Did God think less of women? No, not at all! He simply used man as man and woman as woman.
The greater part of this history was played out long before the Church came to be. The institutions of marriage, the family, the home, and the government were already established with men in the leadership roles. The business of governance, of war, of judging, etc. was given to men. The coming on the Church did not change that but only reinforced it with specific admonitions against women leadership in the Church. When, God, in the person the Son, came to earth He came as a male.
No doubt God used women in His will as He did men but their roles were not the same and the exceptions were very few and for specific situations. No doubt courageous intelligent capable women have served in interim times of history but those are the exceptions for whatever reason and not the norm nor the design. God created man with the attributes for leadership. He created woman with the attributes to help and nurture. He gave intelligence and abilities to both but designed them to lean a bit differently in order to most effective at their roles. Man was created first and then woman. Man needed a woman as a helper and she was created for Him as part of God's plan. God gave man responsibility for woman's actions as is evident by His asking Adam - not Eve - what they had done.
Man has no more inherent value than woman - both are His creations and belong first to Him. Man did not create woman - God did. But God did put man over the woman.
The example is clear from the whole of the Biblical story as well as the specific verses that touch on the subject. It is not limited to the home and to the Church but to life in general.
We shouldn't think we're smarter than God by ignoring the historical record He has given us in His word. We shouldn't make women to feel they are inferior unless than pursue and excel at all the same roles as men and, likewise, we shouldn't do so for men. Men need to step up to their responsibility and not give temptation to women to have to take their place.