symmetry is a rough indicator of genetic health. Your genes split nice and evenly your probably prone to have less mutations to pass on to your offspring. So following Darwin if many generations prefer symmetry we'll find most things symmetrical. Legs are the same length, arms are the same length, face, ect.
But when it comes to things like fur other factors can override the symmetrical preference. Like survivability for example. Cats have been found in many regions so they have varying "fur" genes that have been passed into their breeds. In this case it's a matter of dominant spot genes vs. striped vs. whatever.
I know a geneticist is going to come into this thread and rip me a new one
--edit--
to further complicate cats and dogs is the selective breeding we've done to them. Bah I'm going back to peas.