We are talking two sides of this issue, so it is necessary to make a distinction.
There are two purposes for education, therefore two reasons why someone would pursue it.
One reason is to learn a trade, and the other is for the education itself. It seems that Bishop Williamson thinks that neither is suitable for a woman.
Ideally, a woman would not have to work outside of her home, nor should she be pursuing high-powered positions in finance, business, or the like- that's my opinion. There are many trades that women are quite suited for, however, like medicine, and the single woman who does not have a vocation to marriage should be allowed to pursue such a thing. If the fact that she is single makes some people uncomfortable, then perhaps it is time to invent some new orders of nuns.
Then there is the other aspect of education, which fills part of our duty in this life- to know God. This would be found in a classical, or liberal arts education; the trivium and quadrivium which are prerequisite to studying philosophy and theology. We are rational animals, and our highest activity is the contemplation of God. Both men and women are given the ability for this- we all are men, afterall. To say that "ideas are not for true girls" or that a girl can make a good "imitation" of a student strikes anyone as against common knowledge and sense. A woman would have a need for this kind of knowledge just as much as a man.
Also, a married woman especially needs a good education to be a good helpmate for her husband. Traditionally, the wife was always involved in her husband's work. From the Queen all the way down to the baker's wife, she serves as administrator, governor, and adviser. This was a reality in medieval society- there are paintings of women performing duties that today would be considered "work outside of the home." It is also a reality in the Bible; read the last chapter of Proverbs.
(edited to add: The work that the woman would be involved in in helping her husband is not only his trade, but also the education of their children, since their generation and education cannot be separated. For this she also needs an education beyond simply knowing how to cook and clean, just as a man needs an education beyond working on the cars and mowing the lawn.)
For those who bring up that part of the Summa where St. Thomas says that a woman is not made to be a helper in man's work (because he is helped better by other men) but in the work of generation, I believe that this is misread. True, a woman, as wombed-man is firstly a helper in procreation, but to stop there is to ignore the fact that she is still a man and as such, suited to help her husband in his other work as well. What we must conclude from this is that God could have made other males to help men if there was no need for procreation, but he instead made a wombed-man who could specialize, as it were, in generating and caring for children. No where is this sense more obviously seen in the farmer's wife, who labors next to her husband in the fields and in the care of the animals, etc. Now, it is true that females have a different set of strengths than males, the most obvious of these being a difference in physical strengths, bone structure, etc., the less obvious being different intellectual strengths. Because of these differences, you have a delineation between "women's" work and "men's" work, which are not rules but a matter of culture and custom. If it were true that women were only made to help men in generation, however, then it would be a gross disregard for God if women were to reject motherhood in favor of the celibate life.
I don't know very much about the history of the university, but I do know that the university looked very different after the Enlightenment got a hold on it. The university was not, however, the only place for someone to get an education. Convents and monasteries were the original sources of education, (and St. Theresa of Avila also learned from her father) and it was at the same time that the universities became secularized and Protestantism began to infect everything, that women were pushed away from the freedoms they had gained in the medieval times. The feminists did not reject a Catholic view of women- they rejected the Protestantised view of women. Of course feminists also rejected what Catholic remnants there were left in the culture in regard to women as well, but it is left to us to distinguish between what things those were. Education is one of those things that women had in the high point of Christendom. Of course not all women had it- as all men did not. The vast majority of men and women were not privileged with a sophisticated education.
