Your arms also don't turn your head. Your arms should reflect the coiling of your spine and help your legs to complete the pli . It rotates or spins because torque, or rotational force has been applied. There are different kinds of tops, and I like to demonstrate with the kind of top that you can spin with your fingers. After you have placed it, you begin a twisting movement, right, left, right, left, and then you can give it a final twist to the right, release it, and it will spin.
Turns are no longer a mystery.
And, don't forget we can go to the moon and back. Just quickly pull your arms into 1st position and that will make you turn. I think what your teacher means is not to athletically swing your arms, as though you're swinging a bat. You do need a preparation. The ball bounces because it is pushed to the earth.