By individual education, I mean, for the sense of the word is not precisely defined, such an attention to a child as will slowly sharpen the senses, form the temper, regulate the passions as they being to ferment, and set the understanding to work before the body arrives at maturity. (2.9)
The main purpose of education (for Wollstonecraft) is to strengthen a person's reason so that they can control their emotions. Being able to control our emotions is what separates humans from animals, and the stronger a person's reason is, the better.
It follows then, I think, that from their infancy women should either be shut up like eastern princes, or educated in such a manner as to be able to think and act for themselves. (3.30)
Wollstonecraft thinks that there can't be a middle ground. Either women should be shut away from society altogether, or they should be given the mental tools they need in order to engage the world as rational adults.
The same love of pleasure, fostered by the whole tendency of their education, gives a trifling turn to the conduct of women in most circumstances. (4.24)
Women are raised to look pretty and to seek out pleasure wherever they can find it. But this lack of discipline keeps them from ever learning to control their emotions. This upbringing leads many of them to become petty and cruel.
Girls who have been thus weakly educated, are often cruelly left by their parents without any provision. (4.43)
Sometimes, a young woman's parents will die and will leave her all alone in the world. And without a husband or an education to fall back on, these women basically have nothing to help them survive. Many of them end up on the street or in the poorhouse, when even a little bit of education might have made them fit for a career.
The management of the temper, the first, and most important branch of education, requires the sober steady eye of reason. (4.55)
The only thing that can teach people to control their emotions is the power of reason. People need to understand why they do things if they're ever going to resist their basic urges. They also need to consider the consequences of their actions and weigh the pros and cons.
For this reason, the education of the women should be always relative to the men. To please, to be useful to us, to make us love and esteem them, to educate us when young, and take care of us when grown up, to advise, to console us, to render our lives easy and agreeable. (5.10)
Jean-Jacques Rousseau believes that God put women on Earth solely for the purpose of pleasing men. That's why he thinks that all women's education should be directed toward pleasing men as much as possible and making their lives easier.
Besides, how should a woman void of reflection be capable of educating her children? (5.49)
How can we expect women to make good mothers when we prevent them from sharpening their judgment and developing their minds when they're younger? Let's not forget that in Wollstonecraft's time, children would have spent the majority of their young lives around their mothers and female nannies. In both cases, having uneducated women in these positions will only end up depriving the children of a good upbringing.
I mean, therefore, to infer, that we ought to have a precise idea of what we wish to attain by education, for the immortality of the soul is contradicted by the actions of many people who firmly profess the belief. (5.140)
Wollstonecraft thinks that before we argue about education, we need to think carefully about what the goal of education is. For her, it's fairly straightforward. Education is about developing a person's ability to control their emotions and act rationally.
Nature, in these respects, may safely be left to herself; let women only acquire knowledge and humanity, and love will teach them modesty. (7.35)
Wollstonecraft thinks that all we need to teach women is knowledge and humanity. Some people might think that educating women will inflate their egos, but Wollstonecraft is convinced that one of the main effects of a good education is modesty, since the more you learn, the more you realize there's a lot of stuff you don't know.
Would ye, O my sisters, really possess modesty […] ye must acquire that soberness of mind, which the exercise of duties, and the pursuit of knowledge, alone inspire, or ye will remain in a doubtful dependent situation, and only be loved whilst ye are fair! (7.37)
If women are going to learn true modesty (and not just the appearance of modesty), they need to train their minds to see just how much there is in the world that they don't know. In this case, these women will only be loved and respected while they're still young and pretty. Once they're old, no one will care about them.