The New Testament shows women praying and prophesying in the assembly, hosting churches, being named as coworkers and as a deacon, and in one case being called outstanding among the apostles. It also contains instructions restricting women from teaching or exercising authority over men.
Both sides of this argument hold a high view of Scripture, and it is a mistake to frame it as the Bible against the culture. The disagreement is about how the restricting texts relate to the enabling ones, and how far each is bound to its setting.
1 Timothy 2:11-15, Galatians 3:28, Romans 16
11Let a woman learn in quietness with full submission. 12But I don't permit a woman to teach, nor to exercise authority over a man, but to be in quietness. 13For Adam was formed first, then Eve. 14Adam wasn't deceived, but the woman, being deceived, has fallen into disobedience; 15but she will be saved through her childbearing, if they continue in faith, love, and holiness with sobriety.
Both positions affirm that men and women are equally made in God's image, equally saved by Christ, equally indwelt by the Spirit, and equally given spiritual gifts. Neither holds that women are inferior, and both regard the treatment of women in much of church history as a failure that needs facing.
Complementarian
Men and women are equal in worth and different in role. The offices of elder and pastor, and the authoritative teaching of the gathered church, are reserved for qualified men.
What it claims
Paul grounds his instruction not in local circumstance but in the created order, appealing to Adam and Eve rather than to anything about Ephesus. The qualifications for elders are stated in male terms. This is a difference of function within equal dignity, as the Son submits to the Father without being less than the Father.
Who holds it
The and churches on the priesthood, and among Protestants the Southern Baptist Convention, Church in America, Lutheran Church Missouri , and many independent evangelical churches. Articulated in the Danvers Statement of 1987.
The texts it stands on
1 Timothy 2:12-13 I don't permit a woman to teach, nor to exercise authority over a man, followed immediately by for Adam was formed first.
1 Corinthians 11:3 The head of the woman is the man, in a passage that also assumes women pray and prophesy publicly.
1 Timothy 3:2 The overseer must be the husband of one wife, given in male terms.
Strongest case
It takes the restricting passages as stated and notes that the reason Paul gives reaches back to creation rather than to a local problem, which is harder to confine to one city. It also represents the practice of most of the church for most of its history.
Hardest question
It has to explain Deborah judging Israel, Huldah being consulted by the king's officials over Jeremiah, Priscilla instructing Apollos, Phoebe as a deacon, and Junia called outstanding among the apostles. Critics also press on 1 Timothy 2:15, about being saved through childbearing, which nobody applies straightforwardly.
Holding the map
A fact worth having: the church has revised its reading of Scripture on a comparable question before. Both sides of the slavery debate in the nineteenth century quoted Paul, and the side that won did so by arguing from trajectory and from the whole shape of Scripture. Egalitarians cite that as precedent; complementarians answer that the creation-order grounding makes this case different. That exchange is the actual argument, and it is a serious one on both sides.
It is also worth being honest that this question is often decided by a congregation before anyone opens a commentary, and that people on both sides have been treated badly. If you are working this out, read the best advocate of the view you do not hold rather than the worst.
Questions that press on this one
None of these stands on its own. What you conclude here narrows what you can say there.
