If one has ever seen a Manx cat hop down the stairs, one understand where this question comes from. After all the Manx is a cat that often has little or no tail, has longer hind legs the front legs, and often hops about (due to the difference in leg length). While the Manx isn’t a “cabbit” or cat rabbit hybrid, it certainly makes it understandable why one would ask this question.
The truth of the matter is, cats and rabbits can not cross breed. This does not stop the tails of cabbit hybrids that circulate about. This may come from watching male rabbits try to mate with anything (or anyone, cat, dog, stuffed animal), it may come from unique cat breeds such as the Manx, or it may come from thinking about other hybrids such as the wolf dog, or the tigon (tiger and lioness offspring).
No matter where the idea comes from, it can’t happen. Many people who will tell you no will point out that rabbits and cats belong to different families (genetically). I think this is a valid point, however there are other reasons as well.
For example. Female cats ovulate when they are stimulated by barbs that are located at the end of the Tom’s penis. This stimulation happens due to the physical make up of male and female cats, and can only happen during mating. Rabbits don’t have these barbs. So, even if a male rabbit were to get that close to a female cat, he wouldn’t stimulate her to ovulate. Without this happening, offspring of any sort couldn’t happen.
Along with other information about how close animals have to be related to procreate, it is very clear that cats and rabbits can not mate. Cabbits remain (and will continue to remain) science fiction, hopeful dreams, or silly antics of fun loving people.