Mary Wollstonecraft lived in the 18th century. The way women were treated, and the rights available to them were drastically different than they are now. One of the key factors in understanding Mary Wollstonecraft's view is what the general view of men and women in their society was at the time. The general population seemed to buy into the idea that being able to properly reason, and make rational decisions were what earned your rights. This concept is supported by other philosophers, and doesn't seem to be too far off from a good system to live by, but the way it was applied to the rights of men and women at the time created great inequality.
Men were generally viewed as more reasonable, and women as more emotional, therefore men were given higher priority in regards to opportunities in their educations and many other things. This patriarchal society that Mary Wollstonecraft felt she was trapped in, which she describes as being created by men, for men, held her and many other women back form their true potential. The fact that men made the laws, and decided what was taught in schools just further expanded their misguided views. Sexism, when existing in an society for an extended period of time will naturally expand the issues that are widely accepted.
For example, women being viewed as less than men, and serving no more purpose than cooking, cleaning, and baring children, will eventually create an environment where that is all they are taught how to do. If everyone believed women were only good for one job, they would only ever been trained and educated to perform that one job. This is what was so frightening to Mary Wollstonecraft, because the greater and more wide-spread a belief becomes, the harder it is to change. We may mistakenly believe women aren't as smart as men, and that will never change their capabilities, but if all believe this, then their opportunities as far as education begin to decrease, and our mistaken view becomes an unfortunate reality. The society in which Mary Wollstonecraft lived in viewed men with intrinsic value, meaning that they could merit something of themselves. A man on his own has great worth, and great potential, he could get educated, buy land, find a wife, and create a pretty good life for himself. Even a man, unmarried, and even uneducated, was still considered to hold some kind of potential that simply wasn't acknowledged in women at the time. Women were seen to have nothing more than instrumental value, which simply means they serve a purpose in the sense they can perform a task. Just as one would need a wrench to secure a screw, one needs a women to bare children, or keep the house maintained properly. Women were not able to buy land, and in most cases were not able to be educated to the degree that a man could. They were taken in marriage, and became the property of their new spouse. The husband acquired the wife, and the wife was expected to count herself lucky to be taken care of by a rational, competent, man.
One way Wollstonecraft believed we could overcome the inequality that stems from such a wide-spread sexist mindset is by created more equal opportunities for female education, especially in giving them the option to study the profession of their choice. A major set back that Professor Hansen mentioned in class was the stigma that men always did the heavy lifting and women would cook and clean up after. Girls taking wood-shop classes in high school and the boys taking home-economics is one of the many crucial steps toward overcoming sexism.