This is just a short thought on what the Bible teaches about male leadership, and setting it in contrast to a way that claims to be Scriptural but is not.
The Bible teaches the principle of male leadership. God's Fatherhood is the ultimate basis of all authority. God has what we call 'feminine' characteristics, but He is our heavenly Father, never our heavenly Mother. To say the latter is pagan.
God created the man, Adam, first. First in order, and in authority. This is why Adam's sin resulted in the fall of the human race (Romans 5:18). Eve sinned first (Gen. 3:6), but God did not regard her as the representative head of the race. Adam is a fitting parallel to Christ, because both are the respective heads of their people.
God ordained in the Old Testament that family lines were reckoned through the fathers. God appointed the twelve tribes based on Jacob's sons. The Jewish priesthood was exclusively male, as was Christ's apostleship (some contemporary efforts to prove there was a female apostle are an exercise in breaking the truth to push a secular agenda).
Church elders and deacons are men only (1 Timothy 3:1-13), and the husband is the head of the home (Eph. 5:22).
The Bible teaches a principle of male leadership, for certain roles. Why then should we reject "male supremacism", which is not the Biblical view of male leadership but mimics it?
The Biblical view of male leadership affirms the essential equality of men and women.
Male leadership pertains to task, not superiority of personhood. The Bible teaches that men and women are equally made in God's image, equally sinful and in need of a Savior, equally loved by God, equally redeemed by the blood of God's son, equally justified in Christ by faith, and equally predestined to be conformed to His image (Romans 8:30).
The wicked spirit of male supremacism, in contrast, downplays or even denies these doctrinal areas of Biblical equality. I know of one case where the daughters of a Christian male supremacist proudly claimed to be their father's property.
Their astoundingly wrong self-description reflects a misunderstanding of Exodus 20:17, as if Moses intended to say that a man's wife or daughters are analogous to his donkey. It reflects a failure to distinguish between property and persons, "ownership" versus "under the responsibility of", and illustrates how important it is to take in all of Scripture to properly understand any particular bit of Scripture.
Male supremacism also suppresses the spiritual gifts and talents of women.
By saying this I do not say that women may serve as pastors or elders. The Bible clearly teaches that they may not. But the Holy Spirit gives His gifts to Christian women just as much as He does to the men (1 Cor. 12:4-11), and this includes all the speaking gifts. To call this truth "liberal" is to ignore God's Word.
For example, the Bible does not forbid women from preaching or teaching the Bible. It says that women should not preach or teach the Bible to men (1 Timothy 2:11-14, 1 Cor 14:34). The Lord Jesus' reasons were based on order of creation and the fall, not on conditions in local culture. Christ wrote inerrantly through Paul, and Christ was not a misogynist!
The Bible certainly does not teach that Christian women should not pursue higher education, if possible. It is wise for a Christian woman to have a working skill-set to fall back upon, in case she never marries, or her husband falls ill or passes away.
A church that only allows its women to cook, clean, and provide child-care, and discourages them from studying theology, does not accept what the Bible teaches about women and women's ministries. I would bet that many churches have been saved from male heretics by the church's Bible-knowledgeable women.
Male supremacism posing as the Bible view of masculinity, or of leadership, is the devil's nasty tag-along neighbor. It needs to be told to "shoo", "git", and "buzz off."