THIS just means an exceptional focused hunter. If the dog is a hunting dog, and getting aggressive and you are in an urban region, you have a problem.
If your dog is used as a hunting dog, and not attacking the owner or other hunting dogs, then its a reasonable expectation. so this issue is really about context.
Caesar salad says ” Prey drive is a natural instinct because dogs are predators and hunters – this is something the human has in common with the dog. A dog and a man relate at a primal level better because of this ability.”
But of course it is the owner that decides when play becomes too serious.
Most dogs find cats very curious. A retriever breed dog may chase and corner a cat, but that can just be pure curiosity that will go no further and in fact presents more of a risk to the dog in getting scratched or losing an eye.
The problem occurs when you are talking about big game hunting dogs that are looking to kill things. Anything big or poisonous that they are trying to get may actually end up killing them.
This is when a re-direction of the play into another nicer human friendly activity like finding hidden objects by scent and getting reward are often used.
The theory about conquering all pervasive dog prey on vermin is to slowly approach the dog treeing an animal or cornering or barking down a hole and entice them with positive dog treat rewards. Let them sniff and make a choice – so make sure the scent of your treat is powerful and meat derived.
Getting your dog back on lead and trying to coax them back to a safe distance away from the tree before you get them to sit, lie down or whatever other submissive activity you choose is the end goal.
NOTE – the more ancient the dog breed, the more true that the dog is to its hunting instinct the more independent or stubborn it will be to change its dog behavior. Remember that man created these dogs, and you are working against their strong suite in trying to divert their instinct.
You will never quash it, and it may take a long time to pacify these dogs, to get them to redirect, but that has to be your end goal if you want a manageable dog you can take out safely in public.