I have had a number of gymnasts as students, and pretty much every one of them could jump, some spectacularly. Getting right to the point, it's because of their core strength. Twisting, flipping, all that, requires IMMENSE core strength. If your core is strong, solid, well-held, the force generated by your legs will go into lifting you off the floor, not in flexing your body.
Think of it this way: You can't push cooked spaghetti.
If you stretch out a strand of cooked spaghetti (sauce optional) and push one end of it, the other end doesn't go very far. The whole thing bends, folds up, and your effort goes into that, instead of moving the spaghetti. Now, if you push the end of a strand of un-cooked spaghetti (put the sauce away), the whole thing is going to move, because none of your force went into bending it.
The same for jumping.
If some of the force of your legs goes into bending your body, it is lost as far as jumping is concerned. One of my former students, Megan Smith, took off like a rocket, because her core was so strong, none of the leg force was dissipated by her body bending.
If you strengthen your core by doing things like cambre really properly, some extra ab work, and by consciously holding your center, you'll jump higher.
See you in class.
