A Vindication of the Rights of Woman is, in fact, heavily influenced by Enlightenment ideas. Wollstonecraft was deeply read in the Enlightenment, and this work was written to challenge the highly influential work Emile, written near mid-century by French philosophe Jean-Jacques Rousseau. Rousseau had argued that women were fundamentally different than men, and that they should be educated only in ways that would be pleasing to men. Women, Rousseau thought, were emotional beings, and their role was to provide a emotionally pleasing partner to men, who were forced (unfortunately, Rousseau thought) to grapple with all the problems of modern civilization.
Unlike Rousseau, Wollstonecraft argued that women, like men, were beings possessed of reason, and a woman's education ought to cultivate reason. So, in short, women should be educated in the same way men were. Her emphasis on reason over emotion was more in keeping with the mainstream of the Enlightenment than Rousseau, whose focus on emotion has often led scholars to categorize him as a "proto-Romantic" or even part of a "counter-Enlightenment." Her emphasis on the importance of education is also very much consistent with the Enlightenment. She saw women and indeed all people as products of their upbringing rather than any essential or inborn traits "degraded by a concurrence of circumstances," as she put it, and argued that women, born with reason, should be allowed to fully cultivate it.