Women can and must preach, as the Scripture tells us on many occasions, for example:
but in your hearts honor Christ the Lord as holy, always being prepared to make a defense to anyone who asks you for a reason for the hope that is in you; yet do it with gentleness and respect (1Pe 3:15)
However, in the assembly of the church, Scripture teaches that women should remain silent in regard to public teaching. Obviously this doesn’t apply to singing hymns etc. For example:
For God is not a God of confusion but of peace. As in all the churches of the saints, the women should keep silent in the churches. For they are not permitted to speak, but should be in submission, as the Law also says. (1 Cor.14:33-34)
Men and women are equal before God, but have different roles in the church. This reflects the situation described in 1 Corinthians 11:3:
But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God.
God is the head of Christ and Christ is the head of the church. The church is a cameo of this hierarchy. In the church, man represents Christ and woman represents man. So when the church is assembled together, to reflect this hierarchy, women subject themselves and don’t take a vocal role.
This hierarchy is also reflected in the covering of women’s heads when they pray. Women are the glory of man and a woman’s hair is her glory therefore she should cover the glory (of man) when she prays. Men don’t cover their head when praying in the assembly because they are the image and glory of God and God’s glory should not be covered.
So the symbols are important to follow. The instructions from God for women to be silent in the assembly
(As in all the churches of the saints, the women should keep silent in the churches. For they are not permitted to speak, but should be in submission, as the Law also says. 1 Cor. 14:33-34 )
do not apply to preaching to people, or teaching children etc. We have the example of Priscilla and Aquilla teaching in a private situation, with Priscilla probably being the more significant teacher as her name is mentioned first.