A dog’s inherited instinct would be to chase cats as he’d chase other small animals because dogs are predators but…’dogs and cats can be friends. This isn’t always true and probably depends a lot on temperament and early socialization, but it can happen’.(Victoria Elder, Los Angeles).
Hate? I don’t think so (Michael Lawrence). The word ‘hate’ is incorrect. You might re-phrase the question thus: ‘Do dogs really see cats as prey or is it just a cartoon fantasy?’.
But neither is it a cartoon fantasy because dogs do chase cats and kill them sometimes. It depends as Victoria says on whether the dog is deeply socialised to accept cats and on his/her temperament. Dogs like cats are individuals.
Dogs can be trained relatively easily and sometimes they are trained to attack others including cats.
However, there are hundreds of thousands of examples of dogs and cats living harmoniously together in family homes. Often dogs and cats form very close friendships. Sometimes dogs raise cats as their offspring. There are far more purebred dogs than cats and dog breeders often socialise their dogs to cats. These dogs will regard cats as associates or friends. They accept cats into their pack.
Dogs will defend pack members from outsiders. There is a very cute story on Quora from Joey Dalan. His dog is an “exterminating breed”. In other words he chases small and furry creatures. He visited his best friend’s home and his friend has a gentle, large dog who although not cat socialised was very friendly towards the family cat (who does not want to be friends but accepts the situation).
Despite best efforts to keep Joey’s dog away from the cat an error occurred giving his dog a chance to attack the cat. He charged ar the cat. The large, gentle, giant dog blocked his path, bared his teeth and growled. Joey’s dog stopped short and ran back to Joey. Point made. Dogs protect pack members.
At the heart of the answer to the question in the title is whether the dog is (a) socialised to cats (b) temperamentally suited to being around cats and accepting them (c) not trained to attack and (d) domesticated to the point where the dog’s inner predator is removed through breeding, socialisation and domestication.
The relationship between domestic dogs and a cats is very wide in its variety. There are perhaps millions of households in the United States where there are both cats and dogs living together. If the dog is chasing the cat it’s in play. I don’t have statistics but it would seem that in these homes the dog is more keen than the cat to be friends. This is probably the pack instinct of dogs versus the solitary instinct of cats but this inherited behaviour is very much watered down by domestication.
P.S. Cats are also predators but if the dog is bigger than the cat he is the top predator of the two.