Rousseau in Emile insists that women are "naturally" given to such behaviors as being obsessed with their looks and playing with dolls. He also asserts that women want to be subjugated by men because they are "weaker." He writes that having the same level of education as men is worthless for women, though they should be given some education, if only to be able to adequately raise their children. He says women are the way they are because nature made them that way.
Wollstonecraft attacks Rousseau's ideas sharply in her Vindication. The book is an argument for the better education of women. Wollstonecraft very strongly asserts that women are not, as Rousseau contends, born with traits of vanity, weakness, and the desire to please men. These, she argues, are all learned behaviors, the result of the poor education women receive. She likens Rousseau's assertions about women's failings to the anecdote of the learned pig, a popular but false story in the eighteenth century that a pig could learn to read.
Wollstonecraft is saying that some popular and widely disseminated ideas and stories—such as the learned pig anecdote and the idea that woman are innately inferior to men—are simply wrong, and she takes Rousseau to task for repeating false stereotypes about women. She goes after Rousseau because he was a popular and respected figure, and she thought his views on women did them great damage.
Wollstonecraft completely opposes Rousseau's ideas, stating that with a rational and sober education, girls would not grow up into silly, vain, childish creatures but into good helpmeets for their husbands and better managers of their households, not to mention able to raise sensible daughters.