To the people that are all for this, you have to line breed a lot of species of animals to prevent health problems, and bring out good genetics. Line breeding is a form of inbreeding, not necessarily meaning breeding brother to sister. Good breeder line breed their animals, if they don't, in most cases they end up with a lot of problems and a junk breeding line that can turn into a disaster. I have to linebreed/inbreed with my rabbits and pigeons, and its similar to most other animals. the key is to selectively breed for a specific trait that produces a good quality, healthy animal that best represents its breed. Also if you support something like this, then you are supporting the animal rights system where they just want to put a lot of restictions on animal ownership for both breeders and pet owners. It will only end up punishing the good, not the bad. That is certainly not something I would want.
That said, i doubt that a a law like that would pass. But I will pass it on to the anti-peta and pet-law yahoo groups.