This is a very tricky question. Mainly due the the fact that people tend to become very sensitive with anything that seems to involve a "battle of the sexes". I assure you, however, this has nothing to do with those issues. This is going to be a blog on the practicality and reality of women teaching men; and in particular the classical male voice.
It is important to point out some facts regarding the classical male and classical female singing voices. First, men sing in chest voice for their whole range. Women sing in headvoice for most of their range, except for the lower notes below F#4. secondly, the male voice develops, generally, a heavier instrument during puberty. You will notice that the thyroid cartilage increases in size and also the voice lowers considerably as the vocal folds thicken. Therefore their voices are heavier and deeper than a woman's voice. Chest voice is when the thyroarytenoid muscles is dominantly active. Headvoice has less thyroarytneoid and the cricothyroids are more dominant. Headvoice is therefore a lighter sound than chest voice.
Since men sing in full chest all the way up to their highest notes, they also must master what is called the "covered" voice. This makes it possible for the chest voice to stay dominant all the way up. This voice is what Corelli, Pavarotti etc. described as being crucial for the high notes. Women do not sing in this covered voice. So they have no practical way of understanding what it is and how it works. They can understand this voice intellectually, but they cannot and do not sing in this voice. This makes it a very difficult endeavor to teach it because a teacher must be able to demonstrate the correct sounds. This is why the greatest male singers in history were taught by other men. Pavarotti, Gigli, Caruso, Di Stefano, Volker, Mardones, Ruffo, Siepi, Del Monaco, Corelli and so on. In fact, I cannot name a single great male singer of the Golden Age who was vocally developed and trained by a woman. There very well might be an exception, but I do not know of one. And this is due the the reasons I described above.
On the other hand, a man can teach a woman to sing with great success. The reason being is that a man sings in chest voice and headvoice. Therefore, it is easy for him to understand both voices intellectually as practically. And male teachers have taught some of the greatest female singers in history. Since women do not "cover" in the way men do, it does not work the other way around. Unfortunately. It would be great if it was possible, but I firmly believe that it is not possible. At least not on a very high level. However, I do believe that women can certainly teach men how to sing to a degree. They can teach them how the breathing works, what chest voice is, how to get core to the sound, what vibrato is and what headvoice is etc. They might even be able to teach, to a degree, some of the "covered" voice in that they could get them to sing EE or OO higher in their range. There is much more to it than that though. You have to move to the other vowels, it is a process getting to them, you have to learn how to sing mezza voci sometimes covered, sometimes you must exaggerate the cover in areas and so on.
None of this is to dissuade women from teaching men at all. I think they can do a very good job up to the point where the covered needs to be worked on. So perhaps younger male singers can learn well the foundations and development from a female singer, but eventually the covered voice will have to be worked on and mastered. This will take working with a skilled male teacher who can sing in the covered chest voice, has developed that voice himself, and knows technically how to do it. This is also not a put down to women, but rather a reality. There are many things a woman can do that a man cannot do. Or things she can understand more than a man because she can do them. It is what it is. That is what makes us different.