“Spontaneous mutation” breeds

A mutation is any unexpected deviation from the norm. A certain cat is born with an odd trait. By mating that cat with a cat with the same odd trait, an entirely new breed results, all the offspring of which have the same odd trait.

The most famous example of this is the Manx, the tailless cat. A more recent example is the Scottish Fold, with the famous flattened-down ears. No one knows what causes genetic oddities, and not all of them are attractive enough that humans would want more of them.