Right, which means you don't actually end up spinning at all, you just contort in an amusing manner.
A diver (and a cat) can only change the direction and speed of the rotation they have upon leaving the diving board. At all times (assuming they aren't going fast enough to use the wind) they must conserve angular momentum. If dropped with no rotation whatsoever, the most skilled diver in the world would be powerless to rotate until they caught some wind. Likewise, if you dropped a cat perfectly evenly with its back to the ground, it would not land on its feet.
In the diver's case, the appropriate rotation is gained from the diving platform, and the cat relies on the complex, chaotic nature of the universe to insure that it will have some angular momentum to work with when it falls off things. :)
Now, if you had a fast canopy, you might be able to help yourself by sticking alternating arms out, much like doing a barrel roll in freefall.