Cats (and scientists) like the say that cats rule and dogs drool. Dogs don't have a response, because they're too busy drooling.
In A Dog's Purpose, we get a dog's-eye view on what Bailey and Ellie (the same dog if you just ended up here and missed out on the whole reincarnation thing) think of their feline frenemies.
The first cat the dog meets is Ethan's cat Smokey. This tabby is Bailey's nemesis: he hisses and spits at him whenever he approaches. Smokey and Bailey tear up the house, but only Bailey gets in trouble—he doesn't understand yet that cats get away with everything. When Smokey dies, Bailey doesn't care. It's not because he's cruel, it's just that he doesn't really understand the gravity of death. And he always thought he was the superior pet, anyway.
As Ellie, the dog has to live with three cats: Stella, Emmet, and Tinkerbell. Stella and Emmet die over the years, but Tinkerbell clings to life like a fairy to her wings. Alone, Tinkerbell looks to Ellie for comfort. Ellie reluctantly gives it: "I didn't understand her attachment to me and knew it was not my purpose in life to be the substitute mother for a feline, but I didn't mind it much and even let her lick me sometimes because it seemed to make her happy" (24.35).
In this one little moment, Ellie the dog learns what it's like to have a pet of her own. All she needed was faith, trust, and a little bit of cat dander.