To my understanding, Paul’s argument on the need for a head covering is based on the principle of theocratic headship, which he stated at 1 Corinthians 11:3: “The head of every man is the Christ; in turn the head of a woman is the man; in turn the head of the Christ is God.” So the head covering becomes necessary for a woman when she is performing some function or duty that normally should be performed by her husband or by a dedicated Christian brother, and that she is performing in a temporary way or due to special circumstances. It shows that she is not usurping his headship.
The important thing is not the head covering in itself, but the heart attitude and proper theocratic conscience of the woman wearing it. She appreciates that this is God’s arrangement, and wears the head covering primarily out of respect for God and His arrangement of things as far as the sexes are concerned. God has assigned the man his role as family head, but this is headship and should not be confused with dictatorship. It only means that he has responsibilities towards his wife and family members under his roof.....it is not a position of power, though some have seen it this way.
In Genesis the woman was created as a "complement" of the man....meaning that the two made up a partnership, neither of which was balanced without the other.
A woman can have a good conscience in this matter only if, besides wearing the head covering at the appropriate time, she has a wholesome respect for the one whose headship is being honored by it.
My 2c worth....