Let me start out a Scripture that is going to seem totally demeaning at first, but I'll explain the principle after:
"As in all the churches of the saints, women should be silent in the churches. For they are not permitted to speak, but should be subordinate, as the law also says. If there is anything they desire to know, let them ask their husbands at home. For it is shameful for a woman to speak in church. Or did the word of God originate with you? Or are you the only ones it has reached?"
1 Cor 14:33b-36 (NRSV)
The modern debate over the passage usually focus on the part that says "women should be silent." The part I want to emphasize here, is "If there is anything they desire to know, let them ask their husbands at home." This is better than the KJV rendering "if they will learn any thing," since the church was a place were women could learn. A clearer translation might be, "If they have any questions, let them ask their husbands at home."
This isn't a direct prohibition of women teaching other women, however follow the logic: women are to be subordinate in the church to the teaching of the men, rather than the other way around.
Another important verse here:
"Likewise, tell the older women to be reverent in behavior, not to be slanderers or slaves to drink; they are to teach what is good, so that they may encourage the young women to love their husbands, to love their children, to be self-controlled, chaste, good managers of the household, kind, being submissive to their husbands, so that the word of God may not be discredited."
There would seem to be a place for women teaching other women here, in the context of older women teaching the younger, to be wives and mothers. However the picture is one of older married women tutoring the younger. What of older single women and widows? The NT gives us a rich picture of such older single ladies serving in a working capacity, rather than a teaching capacity.
Now for the rub. It would seem from these verses like there is a place for a women's ministry. The problem is, we in the West like to institutionalize church to the Nth degree. Every good and perfect thing gets turned into yet another ministry at the church-house. This is hardly what would be seen in the early church. Women taught women not in the assembly, but in the context of the home and daily life and fellowship (see John Gill on Titus 2:3). The difference may seem trivial but it is not.
Institutionalized women's ministry fails in several ways:
1. It abstracts the Christian woman's concept of Godly womanhood from her place as a wife and mother.
Who a Christian female ought to be is dependent on her relation to marriage and motherhood. With a single female, this isn't a huge issue. With those who are married, the relation is one of following her husband's direction and caring for the house and children. Women's ministries result in women substituting the seeking of direction and guidance from the husband and based on what the family needs, to whatever vision of womanhood is being presented in Bible studies and classes, which may not be entirely appropriate for her home.
2. It results in comparison and stratification.
Who has the best marriage, who has the best kids, who does the most in ministry. Who gets to teach, sing, etc. in the church. Who is married to who is higher up in the church... As the above issue of abstraction sets in the circle of church women becomes the mold around which a new form of womanhood gels.
3. It results in dissatisfaction with husbands and children.
The backwash of number 2 has women critiquing why their husband and children can't be like so-and-so's family, who always seems so perfect when you talk to her, hey, that's why they let her teach the women's Bible study sometimes. If only my family could be better, I could get to lead a ladies' function...
4. It results in a shift in focus from family to church.
As a result of all the above, and further eroding her presence in the home.
The Biblical admonition "women ... should be subordinate ... If there is anything they desire to know, let them ask their husbands at home." is wise advice. It directs the seeking Christian wife to her husband for counsel and guidance, so she may be what her family needs.
Now I am not advocating that Christian wives be locked in the house. I am thankful she has friends, at church and elsewhere. I am thankful she spends time with them. My wife had a girl's night out this past weekend. My concern is when spiritual direction comes from a handful of ladies at church rather than from me, her husband, and the pulpit.
It's why we don't read books on how to have a physical relationship or how to raise our children. Such things are unique to the personalities involved. What's important is to have your family's heart, and be sensitive to who they are, not following somebody's artificial techniques. That's not to say we don't have questions, but they are highly targeted to specific issues and the effort is made to implement such outside advice in a way that works with our pre-existing structure.