Getting back to the subject of the OP... There is no question that women should teach in the church. Have they been given different gifts than men? Is their understanding of Scripture and God's word less than that of men? Are they unable to communicate God's truth and wisdom to others?
To whom did Jesus give the most important task of communicating God's truth and wisdom ever given?
Matthew 28:1-10, "After the Sabbath, as the first day of the week was dawning, Mary Magdalene and the other Mary went to see the tomb. And suddenly there was a great earthquake, for an angel of the Lord, descending from heaven, came and rolled back the stone and sat on it. His appearance was like lightning and his clothing white as snow. For fear of him the guards shook and became like dead men. But the angel said to the women, “Do not be afraid, for I know that you are looking for Jesus who was crucified. He is not here, for he has been raised, as he said. Come, see the place where he lay. Then [you women] go quickly and tell his disciples, ‘He has been raised from the dead, and indeed he is going ahead of you to Galilee; there you will see him.’ This is my message for you.” So they left the tomb quickly with fear and great joy and ran to tell his disciples. Suddenly Jesus met them and said, “Greetings!” And they came to him, took hold of his feet, and worshiped him. Then Jesus said to them, “Do not be afraid; go and tell my brothers and sisters to go to Galilee; there they will see me.”
Luke 24:1-12, "But on the first day of the week, at early dawn, they went to the tomb, taking the spices that they had prepared. They found the stone rolled away from the tomb, but when they went in they did not find the body. While they were perplexed about this, suddenly two men in dazzling clothes stood beside them. The women were terrified and bowed their faces to the ground, but the men said to them, “Why do you look for the living among the dead? He is not here but has risen. Remember how he told you, while he was still in Galilee, that the Son of Man must be handed over to the hands of sinners and be crucified and on the third day rise again.” Then they remembered his words, and returning from the tomb they told all this to the eleven and to all the rest. Now it was Mary Magdalene, Joanna, Mary the mother of James, and the other women with them who told this to the apostles. But these words seemed to them an idle tale, and they did not believe them. But Peter got up and ran to the tomb; stooping and looking in, he saw the linen cloths by themselves; then he went home, amazed at what had happened."
John 20:11-17, "But Mary stood weeping outside the tomb. As she wept, she bent over to look into the tomb, and she saw two angels in white sitting where the body of Jesus had been lying, one at the head and the other at the feet. They said to her, “Woman, why are you weeping?” She said to them, “They have taken away my Lord, and I do not know where they have laid him.” When she had said this, she turned around and saw Jesus standing there, but she did not know that it was Jesus. Jesus said to her, “Woman, why are you weeping? Whom are you looking for?” Supposing him to be the gardener, she said to him, “Sir, if you have carried him away, tell me where you have laid him, and I will take him away.” Jesus said to her, “Mary!” She turned and said to him in Hebrew, “Rabbouni!” (which means Teacher). Jesus said to her, “Do not touch me, because I have not yet ascended to the Father. But go to my brothers and say to them, ‘I am ascending to my Father and your Father, to my God and your God.’ ” Mary Magdalene went and announced to the disciples, “I have seen the Lord,” and she told them that he had said these things to her."
It seems beyond obvious if the resurrected Savior chose women to go announce His resurrection to His disciples that there should be no question whatsoever that women should teach in the church and everywhere else. Again, Jesus chose women to tell the greatest news ever spoken.
It is a specious argument to claim that this behavior is somehow an invention of modern society.