I see, but if you notice, in the exercise, he uses long lines that go from one edge of the square to the other rather than multiple small lines. He does go slow, and I wouldn't recommend that, especially if you are having trouble keeping a straight line. Rather, use all the canvas, prop up the surface, fake the line in the air (ghost it) a couple of times, and go for a slightly quicker, decisive line when you are more comfortable, using the shoulder rather than hand or wrist. Try keeping a firm but not too tight grip so as not to hurt yourself over time but also to keep control. The line that comes diagonally from medial to lateral (using the deltoid mostly) is the one that comes most naturally, if anything, practice that one line and rotate the canvas for other straight lines as you get more comfortable with weird angles (such as pushing towards medial or lines that go vertically)
cheers