Wollstonecraft spends the first third of Vindication talking about the general rights of humanity. For her, human rights are due to anyone with the ability to reason. You got it: we all have the ability to reason; it's the ability to reason that makes us human and not simply animals.
Also, states Wollstonecraft, we all have immortal souls. Our souls live beyond our bodies and are therefore not connected to our gender in any way. That means that our power of reason (which is connected to our mind/soul, not our body) is something that has no connection to our gender.
Wollstonecraft uses these arguments to show that women should receive the same kind of education as men.
Once she's laid out the basic reasons for women's equality, Wollstonecraft singles out and critiques specific thinkers who have argued that women should only be educated for the purposes of becoming good wives and mothers. She focuses especially on Jean-Jacques Rousseau, a man whose writings were very popular during her time.
Jean-Jacques Rousseau's writings on women's education were extremely conservative, and Wollstonecraft goes to great lengths to point out all of the logical contradictions within them. It's a Rousseau roast, and Wollstonecraft is the host with the most.
Wollstonecraft spends the last third of Vindication talking about how parents and schools can do a better job of educating boys and girls and giving the genders an equal playing field. She states that both parents and schools could do a better job of teaching children how to make rational arguments and how to be morally good. In her mind, self-interest dominates society way too much and we need make steps to make people more compassionate, moral, and rational.