It's not really a matter of chasing CATS - it's just a fact that dogs chase things that move. It is part of their instinctive behaviour. Balls, rabbits, squirrels, rats (even cars and cyclist in the case of the badly trained). Cats, being smaller, wisely run from the potential aggression of dogs, and that in turn means the average dog will then enter into a chase. Chasing is fun for dogs, and the prospect of eating the item being chased doesn't really enter the equation. When they grow up together, or when a dog has been well-trained, it is perfectly normal for dogs and cats live peaceably together