There are some strongly conservative Christian churches who follow a movement named "Christian Patriarchy". As a result, the words "patriarch" and "patriarchy" take on a controversial note. Those words already are considered negative things in the world, but there's also some confusion among Bible-believing Christians.
"Patriarchy", strictly speaking, means "rule by a father." The human race fell into sin because of Adam's transgression. God set up Israel as a patriarchy. God covenanted with Abraham, Isaac, and Jacob to create the people of Israel. All the covenant heads in God's redemptive plan were men.
God established an all-male priesthood for Israel. God established an all-male monarchy as well. God made the father the head of the Jewish home.
It's true that women had comparatively fewer rights than men (though a great many more rights than women held in the idol-worshiping societies), though I think God intended Moses' Law as a transitional system until the current dispensation of grace.
According to God, He Himself is the heavenly Father, so the universe is being run by a Patriarch. God has qualities we associate with mothers (for example, Christ compared Himself to a mother hen in Matthew 23:37), but God never refers to Himself as our heavenly Mother. God's self-chosen names are all masculine.
The New Testament supports the rule that husbands are the overseers of the home (Ephesians 5:23). Church elders are also men (1 Timothy 3:1-2). Adam was a man, so the Savior also had to be a man.
However, I observe that there are conservative churches (and some who pose as conservative) which overreact to society's liberalism and go too far. Corrupt or oppressive traditionalism is just as sinful as radical liberalism.
God's Word in Genesis (especially chapter 1) starts with the essential equality of men and women. Men and women are equally in God's image, equally lost, equally sinful, and equally in need of the Savior.
Men and women in Christ are equal in redemption, and their standing before the Lord is the same (Galatians 3:28). Christian women and men can receive any spiritual gift, including teaching, even though the audience of the teaching gift is limited for women (1 Timothy 2:11-12).
The Bible's affirmation of male leadership never excuses sin, disrespect, or a demeaning attitude toward women. Nor should a young single women live to please her father,. Her focus should be on the Lord even as she loves and respects her parents. The Bible also does not forbid higher education, or vocational training for single women, nor does it forbid single women working outside the home. It does not forbid women serving in civil government. It does not require a young woman to marry before she can follow the Lord into Christian service. In fact, the Bible does not require single young Christian woman to marry at all (1 Corinthians 7:25-35).
God calls Himself the heavenly Father, and He teaches male leadership. We should not concede this to the secularists. However, we need to be wary of how some ministries abuse the Biblical truth of male leadership -- and have sorely, even criminally, abused women.
We know the shocking power and sex scandals in churches that have dirtied the name of Christ in recent years. We also read about excuses and cover-ups that should never have happened. God requires us to be as stern against the abuse of women as we are intolerant of any other evil.