Actually, as I am sure you are aware, the different "kinds" of animals that you list cannot breed with each other but that is not to say that they did not stem from the same "kind". If you go far enough back you will find an animal that is neither the dog we know today or the cat, but a predecessor of both. This organism diverged into a line that at some point would become a modern dog, and another line which would become a modern cat. Once they had sufficiently diverged those two lines would be unable to reproduce together, even perhaps at some point being capable of mating only to form sterile offspring (such as the mule we are familiar with).
This is what the *evidence* shows us, not wild speculation. Human endeavors into breeding have caused offshoots which are unable to breed with the previous stock; this provides empirical evidence showing how different "kinds" can be created with a common source. I highly suspect that you eat some of this evidence daily.