If Wollstonecraft is anything, she's logical. She's so logical that she won't even begin her argument without laying down some premises that will inform everything she writes for the following couple hundred pages. She opens her book by saying, "In the present state of society it appears necessary to go back to first principles in search of the most simple truths, and to dispute with some prevailing prejudice every inch of ground" (1.1).
Now when she says, "the present state of society," she's referring to the fact that since the American Revolution—and especially since the start of the French Revolution—people have come to question all types of traditional authority and have demanded that laws be backed up with solid reasons. That's why it's important for Wollstonecraft to go "back to first principles" and examine everything from the bottom up, no matter how simple or commonsense some things might seem to be.
The first thing Wollstonecraft wants us to accept is that reason is humanity's most important power. As she says in the book's second paragraph, "In what does man's pre-eminence over the brute creation consist? The answer is as clear as that a half is less than the whole; in Reason" (1.2).
This premise will go on to be super important, since Wollstonecraft believes that the power of reason has no gender, which means that men and women have the same power of reason and therefore should be educated in the same way.
Wollstonecraft isn't just arguing for women's rights. She's arguing against anyone who would be so shallow and misguided to think that women should only be pretty wives and nurturing mothers.
She knows that many people have tried to justify women's oppression. For example, she says, "To account for, and excuse the tyranny of man, many ingenious arguments have been brought forward to prove, that the two sexes, in the acquirement of virtue, ought to aim at attaining a very different character" (2.1). But the fact remains that all of these arguments are groundless. They're simply excuses for the fact that men act like tyrants toward women.
In some cases, Wollstonecraft will admit that some people need to be completely taken care of by others, as in the case of children: "Children, I grant, should be innocent; but when the epithet is applied to men, or women, it is but a civil term for weakness" (2.5). While Wollstonecraft admits that women are physically weaker than men, she states that their souls are equal in strength.
Both men and women have immortal souls, which means that both men and women have souls that exist outside of the physical realm. Bodies die and souls do not. Bodies are gendered and souls are not: that's a main reason why both genders should get the same treatment.
At several points in this book, Wollstonecraft shows us that she feels a close connection with women who've written before her (as well as the ones who'll write after her). When she thinks of another female writer named Mrs. Macaulay, for example, she thinks that, "The very word brings Mrs. Macaulay to my remembrance. The woman of the greatest abilities, undoubtedly, that this country has ever produced" (5.124). Mrs. Macaulay is evidence that an educated women can use her education to write thought-provoking materials.
Wollstonecraft is also really critical toward women at some points in this book. But the only reason she critiques women is because she thinks that women's flaws could be easily fixed by having more access to good education.
She knows that many women won't want to surrender the power they get by being pretty and flirtatious, but she begs them to reconsider their priorities, writing, "Would ye, O my sisters, really possess modesty, ye must remember that the possession of virtue, of any denomination, is incompatible with ignorance and vanity!" (7.37).
This isn't just a question of education for Wollstonecraft. It's a question of morality and goodness.