The paradox arises when one considers what would happen if one attached a piece of buttered toast (butter side up) to the back of a cat, then dropped the cat from a large height.
Some people jokingly maintain that the experiment will produce an anti-gravity effect. They propose that as the cat falls towards the ground, it will slow down and start to rotate, eventually reaching a steady state of hovering a short distance from the ground while rotating at high speed as both the buttered side of the toast and the cat’s feet attempt to land on the ground. This, however, would require the energy that keeps them rotating to come from the gravitational energy expended in the system's fall; otherwise it would violate the Law of Conservation of Energy.
Another theory is that as the cat is dropped and begins to rotate at a very high speed, the butter will begin to fly off of the toast, until it is all removed. Once the butter is removed, the cat will simply fall to the ground on its feet, as the piece of toast on the cat's back is now butterless.