I think the only time a dog should be shot is if you are in danger. You don't have to be an anti for something like this to turn your stomach. It just isn't right. I've had dogs chase deer many times while deer hunting. The deer live with it year round and they do just fine. A healthy deer has no trouble getting away from dogs. After the dogs run past my stand the deer soon go back to doing what deer do. Most times these dogs are not strays but belong to someone even if they don't have a collar. Most people in rural areas don't pen their dogs up. If you can't kill a deer don't blame it on the dogs.