Marriage is a picture of the relationship between Christ and His church.
The woman was told to wear a covering in the gathering of believers and the man was to be uncovered. This had nothing to do with submission to the man by the woman, it is a picture of the woman as the church and the man as Christ.
The picture of marriage and of this observance of the covering for women and no covering for the man was to show the close relationship between Christ and His church.
Christ died for the mankind so that those who trust in Him will work to His good will not their own. The woman is a picture of the church working to support the will of Christ.
Both woman and man serve Christ together, one is not over the other, they are one as Christ and His church are one.
The picture of woman covered and man uncovered is demonstration of the protection and love of Christ toward His church and the church in obedience to Christ. Both are obeying Christ, both walk together to serve Him. One is not greater than the other, they are one together.
Romans 6:5-7: If we become one with Christ in his death, we will also be one with him in being raised to new life.
1 Corinthians 6:17: Anyone who is united with the Lord is one with him in spirit.
Each one has their calling given to them by God. Man does not give them their calling, Christ does that for each. His mandates for the woman and the man in the Bible are different but equal in importance.
The man does not dictate to the woman her job, he leads and instructs and she obeys when what he says is biblical. If the man leads badly and does not obey Christ then the woman must obey Christ first. The same is true of the man, he does not submit to his wife when she does not obey Christ but he does listen to her when she gives godly counsel.
Any man who thinks he is superior to woman is arrogant and self willed, disobedient to Christ. Any woman who thinks she is independent of man is self-willed and disobedient.
When a marriage honors Christ then both will be fully confident in their work without the need to be pressured to do what the other one desires. We seek to please one another but we do not seek to dominate and oppress the other.
Leading is not oppression or intimidation, it is sharing truth and leaving the decision to the one hearing. Following does not mean obeying evil. Christ always comes first in everything.
Ephesians 5:24-26 "…24 Now as the church submits to Christ, so also wives should submit to their husbands in everything. 25 Husbands, love your wives, just as Christ loved the church and gave Himself up for her 26 to sanctify her, cleansing her by the washing with water through the word,"
Each spouse seeks to please God through supporting their spouse when the spouse honors God.
The perverted and worldly idea that men should pressure, badger and intimidate their wives and their wives should just put up with it is not only unbiblical it is monstrous.
Every man ought to realize it is easy to follow a loving protective husband who seeks the well being of his wife. One who encourages her in her calling while supporting her in her freedom to carry out her duties as given by God.
Every wife must acknowledge that her husband has a choice to follow his calling and every husband should acknowledge the wifes has a choice to follow her calling which was given to her by God. Proverbs 31
When husband and wife protect the calling of each in their roles the marriage will be lovely and God will be honored. Not only this but there will be a working together that surpasses any human endeavors.
"Let God be true and every man a liar."
When we seek Christ we will often be at odds with family and the rest of the world. Our culture has dedicated themselves to human traditions that do not honor God but oppress others and suppress the truth of God's Word.
Ephesians 5:33
"Nevertheless, each one of you also must love his wife as he loves himself, and the wife must respect her husband."
Respect is for everyone, those who use manipulation and intimidatrion in any relationship does not have love in their heart. Here is the nature of love as God gave it;
1 Corinthians 13:4-8
"4 Love is patient, love is kind, it is not jealous; love does not brag, it is not arrogant.
5 It does not act disgracefully, it does not seek its own benefit; it is not provoked, does not keep an account of a wrong suffered,
6 it does not rejoice in unrighteousness, but rejoices with the truth; 7 it keeps every confidence, it believes all things, hopes all things, endures all things."