Its very important to hold to the Word of God so that we dont twist the truth that we have been established upon through Christ, and we must verify such things according to the scriptures.

Stepping back and looking at the big picture; Mankind (both male and female) is like unto Eve(woman)... And Jesus is like unto Adam(man), yet where Adam failed and gave into sin, Christ did not, and remained sinless to His death and resurrection even for eternity to come.

1 Corinthians 15:45 So it is written: The first man Adam became a living being; the last Adam became a life-giving Spirit. 46 However, the spiritual is not first, but the natural, then the spiritual.
47 The first man was from the earth
and made of dust;
the second man is from heaven.

Christ payed the dowry (which was His death) for His marriage (unification) to His church (all believers both male and female), His people, His love, His bride.
When it comes to spreading the gospel, we do nothing. But by faith Christ spake for us, and through us. The apostles continuosly reassured us of that.

Galations 2:20 i have been crucified with Christ, therefore it is no longer i who live, but Christ lives through me. And the life i now live in the flesh, I live by faith to the Son of God who loved me and gave Himself for me.

According to Gods Word, speaking is not permited for women in the church, women are to be silent in their role in the church and if they need anything they are to speak to their husband (whether it be a man or directly to Christ). They are to know what needs to be done and act accordingly not needing to speak a word.

1 Corinthians 14:34 The women should be silent in the churches, for they are not permitted to speak, but should be submissive, as the law also says. 35 And if they want to learn something, they should ask their own husbands at home, for it is disgraceful for a woman to speak in the church meeting.

When Eve(mankind) enticed Adam to sin, he could have denied, but he respected and trusted in the woman that God made for him out of his bone and his flesh, and so he also became a sinner like Eve(mankind). And for that they were both cast out... Which is a prime example of why women should be silent when it comes to the church because they are far to influential for men to over come their desire to please them...

1 Corinthians 7:32 I want you to be without concerns. An unmarried man is concerned about the things of the Lord, how he may please the Lord. 33 But a married man is concerned about the things of the world, how he may please his wife, 34 and his interests are divided. An unmarried woman or a virgin is concerned about the things of the Lord, so that she may be holy both in body and in spirit. But a married woman is concerned about the things of the world, how she may please her husband. 35 Now I am saying this for your own benefit, not to put a restraint on you, but because of what is proper and so that you may be devoted to the Lord without distraction.

Men have a natural urge to please women, and women entice men to act in a way that they would not usually act. And even though men can be foolish, women are supposed to be faithful and meek in their actions, subserviant to God, and if they're married be subserviant to their husband.

In Exodus 4:24-26, Zipporah (Moses' wife) saved Moses by her faith... Because Moses did not fulfill the covenant of Abraham by circumcising their son Gershom, the Lord God came to kill Moses, so immediately without speaking or being told what to do, Zipporah took a sharp stone and circumcised their son.
Then all she said to Moses was "you are a bridegroom of blood", which was acknowledging him as her husband before the Lord, sparing him from death by her faith...
That was a foreshadowing of:

1 Corinthians 7:13 Also, if any woman has an unbelieving husband and he is willing to live with her, she must not leave her husband. 14 For the unbelieving husband is set apart for God by the wife, and the unbelieving wife is set apart for God by the husband. Otherwise your children would be corrupt, but now they are set apart for God.

I understand that coming at this issue from a feminist approach can lead to some twisted idealism about men.
So the fact of the matter is... Men do not "crave" to rule over women, they desire to rule for women, to provide for them and please them, because men are more concerned with pleasing their woman and making her happy rather than pleasing God. And a woman would be more concerned about pleasing her man rather than pleasing God.