Wollstonecraft firmly believes that the government should create some sort of public school system where children from all walks of life come together and learn. She would turn out to be pretty right-on about this, because what she's describing here is a blueprint for our modern school system.
Wollstonecraft doesn't approve of private schools because by their very nature, they teach children to think of themselves as different from the children who can't afford to go. She also doesn't approve of homeschooling, since the absence of other children leads the student to think that she or he is the most important person in the world.
One thing that Wollstonecraft thinks is horrible for society is the fear of change and innovation. She constantly mourns the fact that schools still teach children to memorize and nothing else. What can we possibly expect of kids when school is nothing more than a contest where the prize goes to the best memorizer?
Wollstonecraft takes an opportunity here to jab at Catholicism, saying that this religion is based completely on groundless authority (i.e. the Pope). Protestantism, she says, is based on the idea that anyone can read the Bible and judge for themselves what it says.
We live in a culture where everyone's goal is to rise one class above whatever class they're in.
Many people might argue that social inequality is a good thing because it allows the most talented people to thrive. But Wollstonecraft is certain that there's no point in sacrificing the majority in order to produce a select group of brilliant people.
Family life and early education isn't necessarily bad. It can be used to create compassionate and brilliant people. It just needs to have the right mix of independent thinking and social responsibility.
How much time do we waste getting kids to recite formulas and historical events that they do not understand? A true public school system would focus on the how of knowing, not the what. Unfortunately, society is just filled with a bunch of parents who want their kids to get gold stars and to beat the other kids. Knowledge isn't the priority.
By this point, it might seem as if Wollstonecraft has gone a bit off topic, considering that this book is supposed to be specifically about the rights of women. Now she brings us back by saying that all of the awful things about the current education system affect girls worse than boys.
So here comes a really radical suggestion. Wollstonecraft thinks that boys and girls should attend the same schools. Gasp. The horror! Wollstonecraft is convinced that the only way to create equality and respect between men and women is to socialize them together from a young age.
Educating women differently couldn't possibly have a bad effect on them, since in Wollstonecraft's mind, there's no possible way anyone could make them weaker than their current education already does.
Wollstonecraft thinks that educating boys and girls together would also have the added benefit of creating early marriages. She tends to think that the earlier two people get married, the better.
Above all else, women must learn self-respect, and they can only learn self-respect by learning to think for themselves. Then they won't spend their lives using seduction and other tricks to get men to give them what they want.
And here's a funny idea. Wollstonecraft wants punishments in the school system to work the same way that punishment for adults does. Any time a student does something wrong, they will have to be put on trial in front of a jury made up of other students.
Wollstonecraft wants stronger laws preventing cruelty to animals, because it's this same cruelty (this same lust for power over another creature) that leads many young people to become cruel adults, too. That said, she has known women who loved their dogs very much and barely paid attention to their children.
In order to be good people, both genders have to act according to the same moral principles. There isn't one set for boys and one for girls.
Not only does society need to educate women and help them become more rational, but it also needs to stop insulting women who do manage to show a little reason. Wollstonecraft herself got called a "hyena in petticoats" by a politician named Horace Walpole because he thought her style of argumentation was "unladylike." Even today, an opinionated and assertive woman might get called "bossy" for doing stuff that would get a man lauded as being "a leader."