They most certainly can! And please, men, come down from your pedestal and stop saying they can't!
Here are the verses which so many conclude is a Biblical prohibition of women teaching men: "Let a woman learn in silence, with all submission: for I do not allow a woman to teach or to be assuming over the man; but let her remain in stillness." (1 Timothy 2:11-12)
Yes, there are behaviors expected of women clearly specified in scripture, but there are behaviors expected of men too! But when you read 1 Timothy 2:11-12, please take the time to understand the context before you conclude these two verses are a prohibition of women teaching men! I assure you, Paul did not say that "women can't teach men", rather, he was declaring what needed to be stated to Timothy, so he, Timothy, could properly spread the Gospel in Ephesus!
So what is the context?
Turn to 1 Timothy 1:3-4:
"When I was going into Macedonia, I requested you to remain at Ephesus and to charge certain persons not to teach different doctrines, and not to throw themselves into fables and stories about genealogies of which there is no end, which produce contention rather than edification in the Faith of Elohim."
So already we know that in Ephesus, false doctrine, fables and stories were being taught, and Timothy was charged to "get this under control". Indeed, we learn a bit more in verses 6 and 7: "But from these some have strayed and have turned aside to vain words; because they wished to be teachers of Torah, while they understood not what they speak, nor the thing about which they contend." Here we see that Timothy was having to deal with people who were trying to teach Torah while they neither understood Torah nor the subject they were addressing!
We must keep this charge to Timothy in mind as we read on in the letter. When we get to 1 Timothy 2:3-4, Paul says "For this is good and acceptable before Elohim our life-giver, who would have all men live and be converted to the knowledge of the truth." So here again, we see that Timothy is being told that Paul is seeking that only "truth" be presented and not the myths and fables. Paul goes on in verse 7-8 to say "...of which I am constituted a herald and apostle. I speak the truth and do not lie, for I am the teacher of the Gentiles in the belief of the truth. I desire therefore, that men may pray in every place while they lift up their hands with purity, without wrath and without disputations." Paul would have no need to say this to Timothy if it were not a problem in Ephesus that gatherings were being disrupted by wrath and disputation. We are not told what these issues are, all we know up to this point is that Timothy has been charged with trying to get the situation under control.
But Paul continues by speaking to one of the issues! He says (verses 9-14): "So also, that women (appear) in a chaste fashion of dress; and that their adorning be with modesty and chastity; not with curls or with gold, or with pearls, or with splendid robes; but with good works as is becoming to women who profess reverence for Elohim. Let a woman learn in silence, with all submission: for I do not allow a woman to teach or to be assuming over the man; but let her remain in stillness." What do we learn here? There is so, so much! At last we have a concrete example of the problem Timothy was facing.
Paul said, right after he said "Worship should be held without wrath and disputation", that "women need to be modest in dress, and stop disrupting!" Clearly, this was one of the problems in Ephesus. Women were not behaving as women of Torah were expected to behave, and they were "speaking out" in gatherings when they should not be speaking or usurping the authority of the congregational leaders. Indeed, the (gentile) women were dressing inappropriately and saying things they should not be saying, otherwise, Paul would have had no need to cite the behavior. What could they possibly be "speaking out" about that was so offensive?
Paul alludes to the issue in the very next verse! He says (verse 13) "For Adam was first formed, and then Eve. And Adam was not seduced, but the woman was seduced and transgressed the command." Huh? Where did this come from? Why would Paul mention Adam and Eve here? To understand, let's look again at the context. This time, historically.
Remember, Timothy is in Ephesus. This is a Greek town deep in the Mediterranean area of the Greek empire. Know also that the purpose of Paul's and Timothy's mission was to spread the Gospel to the gentiles. So here in Ephesus, Timothy was trying to coordinate the teaching of Torah and the Gospel to gentiles who themselves were mired in the ancient and false teachings of Greek life. And that Greek life included many false doctrines of false gods. Indeed, one of the false teachings at this time was the myth that women were like Eve ("Zoe" in Greek) and that it was women who were created first! The myth taught that women brought spiritual life to man and demonstrated that the creator of the world was not the true God. This is a form of Gnosticism and was prevalent in the Greek empire at this time, and it was this sort of teaching that gentile women were bringing with them to gatherings. Now we understand why Paul said: "For Adam was first formed, and then Eve. And Adam was not seduced, but the woman was seduced and transgressed the command" in his letter to Timothy! This was clearly a direct reference to a false teaching in Ephesus, that was one of the disruptions of which Timothy had to prevent.
Now we know the whole context of 1 Timothy 2:11-12! It is not a blanket prohibition of women teaching men! It is but an example of how Paul controls the congregation so only truth is permitted in a locale where much false teaching is prevalent! Remember Timothy's charge in 1 Timothy 1:3-4 (above). Still there is more evidence that there is no blanket prohibition of women teaching men. It is found in Acts.
In Acts 18:24-26, Luke writes: "And a certain Jewish man from Alexandria named Apollos, who was trained to eloquence, and well taught in the Scriptures, came to Ephesus. He had been instructed in the ways of Master YHWH, and was fervent in spirit; and he discoursed and taught fully respecting Y’shua, while yet he knew nothing except the immersion of Yochanan. And he began to speak boldly in the synagogue. And when Aquila and Priscilla heard him, they took him to their house, and fully showed him the way of Master YHWH." Here we find a woman (Priscilla), teaching a man about the Gospel of which the well-schooled Jewish man was unaware. If there was a prohibition against women teaching men, Luke would surely have known about it and he would have admonished Aquila and Priscilla. Yet he said nothing. Surely, if women were not to be teaching men, he would have indicated it here! He would have said something like "...this unrighteous woman blasphemed the Lord by teaching Apollos!" But he said nothing of the sort. And Paul mentions the help of women in spreading the Gospel in Romans, 1 Corinthians, Philippians, and Philemon.
No, all Paul cared about in his letter to Timothy was the proper teaching of truth to the Gentiles. (See 1 Timothy 2:7) To this goal, he had to ensure the synagogues were not disrupted by false teachings and by gentile women who saw the opportunity to compare themselves to "Zoe" by their Greek upbringing. Paul most certainly understands the role of both women and men, indeed he goes on in his letter to define the qualifications of the elder. And he discusses the qualifications of a righteous woman and her role in teaching the young. He says all this so Timothy can bring about good order in Ephesus. But while Paul held to the traditions of male authority in the Synagogue, Paul, like Luke, does not seem to be the kind of man who would deny a qualified woman - who knew Torah and her role - to teach men when it was appropriate. And there is most certainly no prohibition against it.