Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Exposition (Initial Situation)
Wollstonecraft opens the book by establishing three basic premises that she'll rely on for all of her arguments. First, she says that humanity is special because it has the power to overcome its animal instincts with the power of reason. Second, the one thing that makes one human being better than another is virtue or moral goodness. Third, the reason we have passions and emotions is so we can use reason to overcome them and gain knowledge in the process.
These are the three core principles that Wollstonecraft needs us to accept, because she suggests that every observation she makes for the rest of this book will come from the understanding of these fundamental concepts. Sounds pretty logical, doesn't it?
Rising Action (Conflict, Complication)
As her argument ramps up, Wollstonecraft claims that the worst force oppressing women is the idea that women should receive a different education than men. Women's education circa 1792 tends to focus only on making women as pretty and pleasing as possible to men, whereas men get educated in all sorts of handy-dandy stuff like science, math, literature and other actual academic subjects. Learning philosophy > learning how to smile properly.
Wollstonecraft singles out several people who have written on this subject and endorsed traditional views on women's education. She totally rips into them and argues that their arguments are hypocritical and not based on any sound evidence at all. For example, why should you have to encourage women to play with dolls and be feminine if this is something that's supposed to come naturally to them? It's this kind of chopped logic that Wollstonecraft can't stand.
Climax (Crisis, Turning Point)
Wollstonecraft isn't going to settle for just improving women's education. She wants to improve all of education, so she argues for the creation of a national public school system that boys and girls will access equally, for no charge. The schools will be paid for by public taxes.
In other words, she's describing our modern public school system. She claims that if society is ever going to advance and become a rational democracy, we need to educate the masses. The moment public education crumbles, so does democracy.
Falling Action
In the closing parts of Vindication, Wollstonecraft speaks directly to parents and tells them what they can do to raise better children (and especially better daughters). She is upset at the number of parents who are invested in their kids' success for the sake of their own ego. These parents want their kids to succeed (and other children to fail) in order to make them look good. Think of the stereotypes of the parents of child stars: that's the kind of ego Wollstonecraft is going after. There's no community spirit in this style of parenting. And, for Wollstonecraft, that's exactly the problem.
Resolution (Denouement)
Wollstonecraft closes Vindication by speaking to men and asking them not to be tyrants. As far as she's concerned, there's no way for men to continue oppressing women unless they're willing to openly admit that they're bullies. The problem is that some men might be perfectly willing to be bullies. So that's why Wollstonecraft makes one last appeal to their compassion and tells them that they'll be no better than the worst villains of history if they don't listen to their consciences and give women equal opportunities in society.