Paul is speaking to the Christians in Corinth and it's about public worship. "But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God" (1 Corinthians 11:3). The implications of this verse are found in the rest of the passage. The orderof authority is: God the Father, God the Son, the man or husband, and the woman or wife. The veil or covering on the head of a believing Corinthian wife showed that she was under the authority of her husband, and therefore under submission to God.
Paul is addressing an issue related to the Corinthian culture that was being allowed to disrupt the church. For a woman to have a shaved head was a disgrace (and, in Jewish thinking, a sign of mourning, Deuteronomy 21:12). Her hair was her “glory” (1 Corinthians 11:15). In the Corinthian culture, women normally wore a head covering as a symbol of their submission to their husbands. Paul affirms the rightness of following that cultural mandate—to dispense with the head coverings on women would send the entirely wrong signal to the culture at large. In fact, Paul says that, if a Christian woman refuses her head covering, she might as well shave her hair off, too (verse 6). A woman who refused to wear a covering in that culture was basically saying, “I refuse to submit to God’s order.” Therefore, the apostle Paul is teaching the Corinthians that hair length or the wearing of a “covering” by the woman was an outward indication of a heart attitude of submission to God and to His established authority.
God's order is that the husband is the head of the wife as God is the head of Christ, but there is no inequality or inferiority implied. God and Christ are equal and united, just as the husband and the wife are one. This is not a passage that teaches the woman is inferior to man or that she should be submissive to every man. It is teaching God's order and spiritual headship in the marriage relationship. In the Corinthian culture, a woman who covered her head during worship or when she was in public displayed her submission to authority.
In today's culture, we no longer view a woman's wearing of a head covering as a sign of submission. In most modern societies, scarves and hats are fashion accessories. A woman has the choice to wear a head covering if she views it as a sign of her submission to the authority of her husband. However, it is a personal choice and not something that should be used to judge spirituality. The real issue here is the heart attitude of obedience to God's authority and submission to His established order “as to the LORD” (Ephesians 5:22). God is far more concerned with an attitude of submission than an outward display of submission via a head covering. First Timothy 2:9-10, "I also want women to dress modestly, with decency and propriety, not with braided hair or gold or pearls or expensive clothes, but with good deeds, appropriate for women who profess to worship God."
Furthermore, how would you apply 1 Corinthians 11 to unmarried Christian women? Was Paul saying they too must wear a headcovering during public worship? Insisting that women cover their hair in church reminds me of churches where traditions and man-made rules and regulations are more important than heart-felt worship. If Christians want to empty their churches overnight, then they should refuse entry to every woman who does not cover her hair. How stupid would that be?