Modesty—Comprehensively considered, and not as a sexual virtue
What would a book about the rights of women be without a chapter about modesty? During Wollstonecraft's time, modesty was one of the greatest qualities a woman could have, since society was fond of women who kept quiet when men were talking. Wollstonecraft wasn't too happy about that, though.
For starters, Wollstonecraft thinks there's a big difference between a person who acts modestly and a person who truly feels humble before God and has a realistic understanding of their own limitations. Unfortunately, women are only taught the first kind.
Any woman who dedicates her life to intellectual pursuits instead of sensual ones (like flirting and playing) will automatically have a purer mind than other women. This purer mind will also make her a morally better person in Wollstonecraft's mind.
A big part of making women properly modest will be to get men to stop hitting on them all the time. Constant flirting pumps up women's egos, and men only do it because they're looking for sex.
Wollstonecraft also thinks that young women tend to get bad habits from nurseries and boarding schools where they sleep and wash in the same rooms as other women. Sometimes, women from the middle and upper classes mix with women from the lower classes, and the lower-class women end up infecting these "better" women with bad habits. In general, Wollstonecraft finds that young women are a little too "familiar" and candid with each other when no parents are around.
Wollstonecraft's ultimate point here is that there's no human quality that women should focus on more than men. Moral virtue doesn't have a gender, and if women need to learn modesty, so do men.