Jean-Jacques was a French philosopher who was famous for his ideas about human civilization and the "social contract" that binds all the people in a society together. He was actually super progressive in some of his ideas; but when it comes to gender, the guy's thinking is as antiquated as it gets.
Wollstonecraft quotes him as saying, "It being once demonstrated […] that man and woman are not, nor ought to be, constituted alike in temperament and character, it follows of course that they should not be educated in the same manner" (5.8).
Or in other words, Rousseau believes that men and women have different biological destinies, which means that society should treat each gender very differently.
Continuing with his thoughts on the genders, Rousseau writes, "The men depend on the women only on account of their desires; the women on the men both on account of their desires and their necessities: we could subsist better without them than they without us" (5.9).
He's saying that women need men more than the other way around, which means that men should pretty much treat women in whatever way they want. But Wollstonecraft isn't about to sit around and let these arguments stand. She devotes an entire chunk of this book to showing why a person's biology shouldn't completely determine what they get to do with their life.
We've pretty much established at this point that Wollstonecraft is not a big fan of Jean-Jacques Rousseau. One thing she can't get behind in this guy's thinking is the way he shrinks away from modern civilization and endorses a return to nature.
As Wollstonecraft writes, "[And] had Rousseau mounted one step higher in his investigation […] his active mind would have darted forward to contemplate the perfection of man in the establishment of true civilization, instead of his ferocious flight back to the night of sensual ignorance" (1.30).
For Wollstonecraft, there can be no question that reason and civilization are what make humanity great. She also argues against Jean Jacques Rousseau's "return to nature" idea, because this return to nature would mean that people would have to rely on their biology (their sex) more than their reason, and reason is what makes us essentially human.
Turning away from the idea of reason is turning away from the essence of humanness. Wollstonecraft is saying that Rousseau's line of thinking is aligned with "Wooo! No toilets anymore, folks! The whole world is our bathroom!"
We can just imagine Wollstonecraft shaking her head and thinking, "Rousseau is such an animal."
Wollstonecraft speculated on why Jean-Jacques Rousseau wrote such harsh things about women. She writes, "And why was he thus anxious? Truly to justify to himself the affection which weakness and virtue had made him cherish for that fool Theresa. He could not raise her to the common level of her sex; and therefore he labored to bring woman down to hers" (12.71).
In other words, Wollstonecraft accuses Jean Jacques Rousseau's wife of being dumb and superficial. Instead of trying to raise her up by educating her, Rousseau decided to argue that women everywhere should be brought down to his wife's level.
This is a really harsh and personal argument for Wollstonecraft to make, and one that's almost impossible to prove. But you can tell just how annoyed she is with Jean-Jacques Rousseau's sexism by the personal nature of her attacks.