Wollstonecraft isn't a big fan of Dr. Gregory, although she's cuts him down a little more gently than she does the other writers she criticizes. She even confesses a certain liking for the guy when she writes, "Such paternal solicitude pervades Dr Gregory's Legacy to his Daughters, that I enter on the task of criticism with affectionate respect" (5.84).
Dr. Gregory was basically a guy who wrote a well-known book about how he would like his daughters to learn traditional "feminine" manners and not to worry themselves with too much book learnin'. Wollstonecraft thinks: "Ew." He also tells his daughters to hide their true feelings whenever possible—ok, says Wollstonecraft, sure: don't let your feelings get the better of you. Fair enough.
But Wollstonecraft draws the line when he says, "Be even cautious in displaying your good sense. It will be thought you assume a superiority over the rest of the company" (5.92).
In other words, Dr. Gregory tells his daughters never to show that they know more than somebody else, especially a man. The worst thing in the world for a woman is to come across as a know-it-all. But Wollstonecraft hates this argument, saying that the person with the most rational mind should be the one who speaks most. She has no time for letting men talk just because they happen to be men.
But the thing that bothers her most about teachings like Gregory's is that they encourage women to focus more on appearances than inner substance. As she writes in her final verdict, "It is this system of dissimulation, throughout the volume, that I despise" (5.96). For her, every human being (male or female) should focus on what's inside instead of outside.