Wollstonecraft’s purpose in citing Rousseau’s theory is to disprove his theory.
To add, in A Vindication of the Rights of Woman: with Strictures on Political and Moral Subjects, Wollstonecraft responds to those educational and political theorists of the 18th century who did not believe women should have an education. She argues that women ought to have an education commensurate with their position in society, claiming that women are essential to the nation because they educate its children and because they could be "companions" to their husbands, rather than mere wives.