The first principle to bear in mind is that feminism is not the standard of truth. Feminism is based on a rotten philosophical foundation of atheism, humanism, and Darwinism. All three of these "isms" are false. As a result, feminism is not the yardstick by which to measure any other systems of ideas. If atheism is true, then there are no fixed, objective moral rules, and therefore there's nothing to judge by. Logically consistent atheists have no moral right to be outraged at anything, let alone be outraged at the Old Testament.
Another way of saying this is that the Bible is not obligated to satisfy modern standards. Modern standards have no authority behind them. They're nothing but fallible people's fallible opinions. The Bible is God's Word, as evidenced by its fulfilled prophecies, accurate diagnosis of the wicked human condition, and transformative power. Jesus unconditionally endorsed the Old Testament. So all contemporary thought must justify itself according to the the Bible, not the other way around.
That having been said, skeptical attacks on the Old Testament's view of women are always guilty of selectivity bias. Only material that appears to demean women is cited (even though, again, the issue of where our standards come from is not addressed). Biblical material that honors women is minimized or completely ignored.
Then is added a multitude of examples of mistreatment of women by the Christian Church through the ages. This last step is irrelevant. The Christian Church, in all its various historical forms, is not the authority of spiritual truth. In addition, the Christian Church disobeys the Bible whenever it truly mistreats women.
Begin at the beginning. The Bible teaches that God created women in His image. Genesis 1:27. Feminism on the other hand, says that women are the random, meaningless results of micro-organisms. Which of those two statements honors and lifts up women?
In Old Testament law, women had God-given rights. They had the right to marital faithfulness (Exodus 20:14). The punishment for attacking one's mother, or kidnapping a woman, was death (Ex. 21:15). An injured pregnant woman was to be avenged (Ex. 21:22-24). Seducers of young single women were punished with fines (Ex. 22:16-17). Jewish society was forbidden to exploit widows (Ex. 22:22-24).
The general moral rules of Moses, such as no committing false witness or not stealing, applied to everyone. Men with skin diseases were subject to the same ceremonial "clean laws" as women with their menstrual periods. Sexual predation was forbidden (Leviticus 11:7-13). Sex trafficking was forbidden (Leviticus 19:29). You don't find these legal protections in the pagan law-codes of the time.
The Old Testament presents a father-centered view of the world because God is a Father, and not a mother. God doesn't have a physical body -- Christ said God is Spirit in nature, John 4 -- so the Bible wasn't talking about body parts. God doesn't have body-parts. Nevertheless, God says He is male. God is not a she, or an it.
God, through Moses, revealed that God created the first human being, a man. God established His covenants with men, and built His people Israel on the foundation of Abraham, Isaac, and Jacob. The father is the over-all head of the home. The Son of God, Jesus Christ, is, obviously, a man. It was impossible for the Messiah to be female.
The New Testament takes a new turn on women's issues, because the Christian Church isn't under Moses' system. Women have greater rights under the Christian system. For example, the apostle Paul says that a single Christian woman can marry any man she likes, as long as he is a Christian also (1st Corinthians 7:39). Unlike the Old Testament law, Paul recommends Christian women remain single. There is no mention in Paul's letters of dowry, or fathers having absolute authority in this area, which is entirely different from Moses' Law.
So we begin to answer this question by rejecting any of the world's "-isms" right out of the gate. The standard of spiritual truth is not conservatism, progressivism, feminism, capitalism, man-made patriarchalism, or any other man-made -ism. The standard of truth is the Bible. The Bible honors women, while at the same time contradicting feminism.