First, let's make sure everyone understands what we want to achieve when it comes to curveballs.
A fastball is thrown with backspin, which is why it stays up (and in some cases looks like it rises). The more backspin you can put on the ball, the more it will stay up.
In contrast, a curveball is thrown with topspin. This topspin is what causes the ball the drop (it creates a region of high pressure on the top and front of the ball).
To put topspin on the ball without supinating the forearm, you have to create the spin using the fingers and not the wrist or the forearm. That is why guys with big hands and long fingers tend to throw the best curveballs.
As I understand it, the way Dr. Mike Marshall wants his guys to throw the curveball is by using a motion that is similar to snapping the fingers. The stronger your hands are, the easier this is to do.