Not all fundamentalist or conservative churches follow Paul's statement about what HE allowed or disallowed in churches. That's the way he put it: "I don't allow....." and his reason was that Eve had been the one deceived. I think Paul was inspired --but he also said in his writings that he sometimes spoke for himself and other times for God. This teaching about Eve was in a letter to Timothy, I believe. I'm not sure Paul thought he was writing God's Word at this point. For one thing, Adam WAS just as deceived by the Serpent as Eve was --in that he believed enough to eat of the tree himself. I can say that --by reading more of the Bible than just a few verses.
When students of the Bible deal with such verses they look to the whole Bible to see how a topic is treated--Paul also wrote that in Christ, "There is neither east nor west, Jew or Gentile (Greek), male nor female, slave nor free --but all are one in Christ Jesus." the implications of this are that women should be treated the same as men in the area of opportunities for service in the church.
Also, scholars note that all of the results of the curse after the Fall, are rightly resisted and diminished by Christians: we resist and fight disease, pestilence, and death and the hardships of work and childbirth --therefore we ought also to resist and ameliorate female subjugation rather than glorying in it as some men and cultures seem to do.
In the Bible we have Deborah as an example of a woman judge who led into battle and was for a time the leader of Israel. There is no condmenation in the Bible for her leadership, so God did not disapprove it.
The Bible says that in the last days the Holy spirit would be poured out on both men and women --and they would both prophesy, i.e. "tell forth the Word."
Jesus was also kind to women and while he didn't choose any of them to be his 12 (would have caused distracting criticism, probably) the Bible refers to various women who were leaders in the faith. I believe that one is listed among some apostles.
Eve was to be a helpmeet beside Adam, a companion made from his side to be at his side.
The Bible says men should love their wives sacrificially as Christ gave himself for the church; and the wives are to RESPECT their husbands as heads of their homes. And as Christians, they are to both be mutually submissive, one to the other ....in honor deferring to one another. this is the pattern for successful marriage in which both husband and wife thrive.
I believe that most women want a man who is strong and leading responsibly in the home --rather than one they can lead about by the nose.
The Bible also says a man should love his wife as his own body.
Oddly enough, some of the most socially conservative, lifestyle strict, Bible-following churches have been ordaining women for 150 years --where as some of the mainline and more liberal groups (including Catholic) held out against equal roles for women in churches, such that it is an issue today for them. Other conservative churches still maintain Paul's restrictions against equality for women as stated in Timothy --but there are too many Biblical exceptions to Paul's rule to make it worth hanging on to.
The person with the biggest Sunday School movement ever was a woman --Henrietta Mears, and she taught and modeled for male pastors in Baptist and other churches how to evangelize and disciple through S.S. Baylor U. lists her in their series as one of the 20th Century's Leading Christian Educators (along with my grandfather, i might humbly add
Women who want leadership in church for reasons of equality come across as masculine and strident, not as people who could lead a church. Women who earnestly desire to serve God and have gifts to use in teaching, should also be free to teach men in their audiences --as Kay ARthur and some other Bible-teaching women have done. Men who have a problem with hearing a woman, are fighting the wrong battle to their own detriment --if the Holy spirit inspires a woman, men should not miss out on hearing the Word of God from any source.