I think that among women you can find wisdom and judgement, but it is rare, just as it is rare among men.
However, even if a woman happened to be the greatest genius of her age it would still not be right for her to be a public teacher, because it undermines the offices of manhood and womanhood, and keeping those offices secure is far more important than individual genius. Not that the wisdom that a woman has should go to waste, it's just that she should offer it in a more private and humble manner than in proudly declaring to a public audience, which is manly.
I watched a young girl yesterday on the internet give a valedictorian speech to her classmates where she went on a lengthy diatribe about the failures of modern education, and it was quite irritating because even though there are plenty criticisms that can be levelled against modern education, it is totally out of place for a young girl to sound these critclicisms against modern education, when she was put in the position of an orator because she applied herself and succeeded in modern education. For a century ago it would have been unlikely that a girl of her age would be giving proud speeches at all, so she has modern education and modernity to thank for that.