It's hard enough for Wollstonecraft to argue against guys who think women should just look pretty and stay quiet. But it's even harder when other women, like the Baroness de Stael, start arguing the same thing. The Baroness is a huge, huge fan of Jean-Jacques Rousseau and she agrees with pretty much everything he says.
She has no interest in women becoming educated because she'd rather have women gain power by seducing men and manipulating them. As she writes of Rousseau, "And in attempting to diminish [women's] influence over the deliberations of men, how sacredly has he established the empire they have over their happiness!" (5.117).
The Baroness de Stael cringes at the thought of women becoming "masculine" by getting the same education as men and trying to participate in public life. For her, this is a throne that belongs to men: "In aiding them to descend from an usurped throne, he has firmly seated them upon that to which they were destined by nature" (5.117).
In the Baroness' mind, the "throne" that women should occupy is the throne of beauty and politeness. She wants women to rule the world by becoming the wives of powerful men and using their influence to manipulate these men.
Basically she buys into the whole "behind every great man is a great woman" thing, whereas Wollstonecraft's reaction is "Hey, yeah: but what's up with this "behind every great man" nonsense? Why can't the great woman be next to the great man?"