Husbands, love your wives, even as Christ also loved the church, and gave himself for it; That he might sanctify and cleanse it with the washing of water by the word, That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish. So ought men to love their wives as their own bodies. He that loveth his wife loveth himself. For no man ever yet hated his own flesh; but nourisheth and cherisheth it, even as the Lord the church: For we are members of his body, of his flesh, and of his bones."
The relationship is clear. It's nothing to do with power and domination. It's nothing to do with servanthood or slavery. It's to do with love, trust, responsibility and support.
If the man is the head of a woman as part of one flesh then what's the use of a head without a body? That question has been answered horribly by the guillotine.
The head cannot digest food. It cannot walk. It cannot pick things up or play the piano.
The body cannot see, hear, smell or taste. It cannot think or guide.
Heads and bodies are necessarily complementary: they cannot exist without each other. The head must use its faculties to care for the body so that the body can support the head. To talk of the head dominating the body is nonsense.
Holy Scripture is clear from the beginning when Eve is taken from Adam. Men and women have different capacities on which the other relies. If only men can be priests then women have to support that in order to receive the nourishing grace of God. But then, priests have to give that nourishing grace not as an example of power-play but for their own salvation.
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Ideas of superiority and inferiority are pagan in origin. They arise as issues of power not of love. Only men can be priests and lead the liturgy and St Paul bids women to submit to that for the love of the Church. That is the way God has ordered things. On the other hand if a priest sees his position as one of power and domination over his flock then he is inperilling his soul gravely. If a priest cannot be a servant to his flock then his view of the priesthood is contemptible - even in the eyes of God who said that he who exalts himself shall be abased.
Misogyny is the hatred of women. There can be no greater hatred of women than for a Society to destroy what it means to be a woman by treating her as a man in issues where that difference is important. There can be no greater hatred of women than to force arbitrary expectations upon them in order to demonstrate that they are women.
The Church sees the difference between men and women as important: there are things that men can be that women can't and vice versa. The key ingredient is not social conformity but nothing less than Love and obedience to God.
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We are all to submit to Christ as our head for we are the Church. Our relationship with Him should be the pattern for our relationships with each other for that is how we know love.
There is no battle of the sexes in the Church. If there is then it is purely pagan!