It’s unrealistic to expect such baked-in behaviours to get “trained out,” and also kind of unfair when you think about it. We bred dogs to love performing these behaviours, and now we’re telling them not to do it? Imagine if someone tried to ban you from doing your favourite activity, like going for runs or playing video games. That’s why, rather than punish predatory behaviour in dogs, it’s better to meet their needs and channel their behaviour into healthy, “legal” outlets. It’s even more natural if you have a breed whose original purpose was one or more of the behaviours in the predatory sequence: searching, stalking, chasing, grabbing, killing, dissecting, and eating. Terriers, for example, were originally bred to hunt small mammals, while the original function of border collies was to stalk and herd sheep. Predatory behaviour in dogs is not a sign of a dog who will be aggressive to people, it’s feeding behaviour - your dog is hardwired to go after critters to eat them, even if he doesn’t actually catch and kill them.