The headship that Paul speaks about in 1Corinthians 11 concerns headship within a family. In a family, the head of a woman is her husband. Christ is the head of both the husband and the wife directly; however, the wife is also under the authority of her husband who is under the authority of Christ. This means that the wife has both the authority of Christ and her husband (who is under the authority of Christ) over her. But, the husband is not under the authority of the wife.
This also means that only the husband is the head of his wife. All men are not the head of all women. A man is the head of only his own wife; not somebody else’ wife. A woman doesn’t need to submit to someone who is not her husband. She is not under the authority of anyone else except her husband, as far as headship is concerned. For instance, the son of a woman is not the head of his mother just because he is male; but, she has authority over her son.
The headship of Christ applies to the Church as a singular body. In this case, there is no difference between male and female. Male members in a church have no advantage over women. The Spirit is not given through gender discrimination; but is poured out upon all singularly and equally. God does not give His Spirit by measure (Jn.3:34).
The headship of man also means that the wife should not try to assume authority over her husband as if trying to disciple him.
And I do not permit a woman to teach or to have authority over a man, but to be in silence. (1Ti 2:12 NKJ)
She is to learn from her own husband in silent submission (1Tim.2:11; 1Cor.14:25).
1Corinthians 14:34 doesn’t imply that any woman is submissive to the males in the church. She only submits to the authority of her husband, and to the God-ordained authority in the church that every man and woman in the local church is equally called to obey. A woman who is in need of learning must ask her own husband at home. She is not permitted to speak (unintelligibly and opinionatedly (lalea –unintelligible talk) in the church. However, she can prophesy and pray (1Cor.11:5,13).