In the opening chapter of A Vindication of the Rights of Woman Mary Wollstonecraft argues that it is in his capacity for reason that man's pre-eminence over the animals ultimately resides. Despite this, however, man all too often allows his reason to be clouded by prejudice. That's certainly the case with men's attitudes towards women.
In their suppression of women, men cynically use their reason to justify their prejudices towards the opposite sex. Wollstonecraft regards this as a serious abuse of man's reasoning powers. Reason should be used to trace, and eventually root out, prejudices, such as those which give rise to women's oppression in society.
Yet largely due to intellectual cowardice, men are either unable or unwilling to do this. This leads them to derive imperfect conclusions on the basis of limited experience and narrow viewpoints. It is just such attitudes that Wollstonecraft hopes to change. What she wants to do is to remove the fog of prejudice that has formed in so many men's minds and replace it with some basic rational principles that, if accepted, will convince men of the fundamental irrationality of keeping women in a state of subjection.
In the final analysis, it is only once the blinkers of prejudice are removed that men will use their reasoning powers as intended and understand that it is virtue, not gender, that exalts one being over another.