If a woman should ever teach a man, they must quote easy and clear verses directly from the bible. This leaves very little room for misinterpretation. Alternatively the women's ideas must be taught by (or came from) a well respected male teachers/pastors/elders, as descried in 1 Timothy 3. These elders must be proven Godly, truly wanting to follow Jesus, by their actions, not merely words.
So this is not about if man is smarter or woman is smarter. Or which sex is better. Not at all. Because at one point in human history, woman was clearly smarter than man. However being smarter didn't help Eve to make things better didn't it? In fact in her "wisdom" she made it worst. Let Adam also eat so he can die with her! What a loving gesture.
Satan would want you to view it as a problem of gender equality. But this is actually a matter of spiritual warfare, of women being more easily deceived than man. Satan will work extra hard against women. Spiritual warfare have no logic or reason, and wisdom without God doesn't help. This is unseen in this world.
That's why it will be impossible to prove in this world. That a woman can be smarter, better and more experienced yet be more easily deceived by Satan. We cannot logic or reason it. We must, in faith, to take the word of God as it is stated.
This doesn't mean women cannot teach men at all (as we seen in the cases of Mary Magdalene and Deborah). But the bible said what it said about woman being more easily deceived by Satan. Hence we have to be careful.