Are cats and dogs mortal enemies? Most puppies pass after cats due to the fact cats run and puppies like to offer chase. My canine Gunny, pictured in my icon, absolutely ADORES cats. Any cat that likes or tolerates a canine gets a heat greeting and kisses from my canine. A lot of pleasant puppies get together with with cats and vice versa. BUT that is so long as the cat thinks they've the top hand. The second the canine attempts to rule the cat, matters change. In a residence wherein the cat and the canine get along. The cat is constantly the boss.