...from Coffman's Commentaries
Verse 12
But I permit not a woman to teach, nor to have dominion over a man, but to be in quietness.
To teach ...
refers to public teaching in the worship. As Nute said:
This prohibition in no way contradicts Titus 2:2,3; it relates to teaching in the church in the presence of men and to the fact that authority in matters concerning the church is not committed to women.
It is upon this verse that the office, either of elder, deacon, or evangelist, must, in the light of New Testament teaching, be denied to women. The wisdom of this is inherent in human nature. Satan, in many instances, has succeeded in creating the impression that Christianity is something merely for the women and children, and not for men at all; and, where such a prohibition as this is denied, the tendency would be to make Satan's lie the truth.
Nor to have dominion over a man ...
This rule is not unreasonable nor capricious. Every entity must have a head, and the headship of man over the family and in the church is by divine appointment. Evil men who do not believe in God, thus rejecting any thought that there even is such a thing as "divine appointment," find it difficult to accept this; but those who believe in God and his word receive it joyfully. In the next two verses, Paul spelled out the reason for God's investiture of family headship and church authority upon men, and not upon women.