From the book of Genesis God makes it clear that man and woman both are humans reflecting that they are equal in terms of rights, authority, duties and responsibilities. Sarah, Esther, Ruth and Mary are the mighty women of Bible and it is no wonder why GOD has biography of Esther and Ruth positioning them with high character and leading ladies.
In modern era woman is educated and occupies great hierarchy levels in the job prospects in politics as leaders, hospitals as doctors and nurses, principal and founder of educational institutions, pastor of the church, CEO and owners of the company where man has to look up to them with respect since they have lower position and less income. Man ought to obey and listen to them in those arenas of profession.
However there is an institution where woman is always second to man ordained by God. It is family. In family man/husband is always at higher level than woman/wife. She may be influential, popular, high income earner and highly educated, but in the family she is wife and has to respect her husband. There are only her children and people younger to her where she can exercise her limited authority below man in the family.
The husband is simply her head, where she has to seek instructions to operate at the family. This is the family wanted by GOD, so man ought to be careful in exercising their authority with love considering their wives as helpers. The wives ought to submit to husbands as they have submitted to Christ. This is gross yet Biblical truth.
Wives, submit yourselves to your own husbands as you do to the Lord. 23 For the husband is the head of the wife as Christ is the head of the church, his body, of which he is the Savior. (Ephesians 5:22-23)