It's true that some dogs and cats naturally get well however not all dogs and cats do. In extreme cases, your dog might try to attack your cat until it dies. If your dog is showing any warnings signs of aggression toward your cat, there is training that can help modify your dog's behavior before it is to late.
The first thing you'll want to do if reduce the prey drive in your dog. If you don't know what prey drive is you'll want to learn first. Prey drive is the instinctive inclination of a carnivore to find, pursue and capture prey. The term is chiefly used to describe and analyze habits in dog training.
Ways to reduce the prey drive in dogs