We do not know the exact conduct Paul was correcting in First Timothy 2:12-15 but the words Paul uses give us a strong hint. The Greek verb translated "exercise authority over" in verse 12 occurs only here in the Bible. However, in secular literature it meant to dominate in an autocratic manner or even to murder. It is possible to read this second verb as modifying the first ("to teach"). In that case, Paul says that a woman is not permitted to teach in a domineering or autocratic manner over a man. (Nor, of course, was even Timothy himself, according to Second Timothy 2:24-25).
In contrast to that, these women are to be "quiet" (v. 12). But Paul does not use the word for "silent" (which he did in correcting disorderly prophets, tongue-speakers and wives in First Corinthians 14), but another word that describes a restful or undisturbed life (see the same word in 1 Tim. 2:2).
I believe that we have allowed a male-dominated culture of the past several
centuries to shape our thinking and cause us unknowingly to misread and misapply
the two passages of Scripture which might sound like they prohibit the public
exercise by women of speaking gifts (1 Cor. 14:34-35 and 1 Tim. 2:12). When we
look at the Scriptures more carefully, we discover that the qualifying principle
for Christian service is giftedness, not gender (Acts 2:17-18; 1 Cor. 12:4-11).