Dog Kills Cats

Question
Our dog, a pit bull mix, has killed 3 cats that we know of and attacked other cats and a baby goat.  He runs for the door when you least expect it, pushes his way out, runs like a bullet (no way to catch him) and makes a bee line to a neighbor's house where a cat resides.  He very, very fast, and an electric fence will not stop him. Do you think there is any possibility, at the age of 8, that he could be trained to follow our commands and stop after he has already headed out the door? He is always leashed when we take him outside, but the problem is how strong, fast, and determined he is to get out the door when we are least expecting it (especially when a guest is coming in or going out, and they don't immediately shut the door), and then his instinct is to head right for a cat and immediately kill it.  Thank you.

Answer
    Unfortnately, a dog who is that aggressive cannot be counted on to stop on command once he is mid chase. There is a possibility of controlling his behavior before he starts the chase, but not once he is in pursuit. He is classified as a level 6 bite dog, the highest level of aggression. He won't ever be safe around other animals. In order to keep this dog under control, you are going to have to enlist the help of an animal behavior specialist. When you are looking for one, check credentials. Make sure they have a valid business license, insurance, and a good track record with rehabilitating aggressive dogs. Ask questions like "How long have you been training?", "Did you attend a school for animal behavior? Which one?", "How do you handle dog fights?" and "What do you do to punish the dogs if they do something wrong?" if their answers make you uncomfortable, find someone else.
    Of course, I am a personal advocate for "positive dog training" methods. However, this is one area where you might consider a remote spray collar for your dog. Spray collars, in my opinion, are more effective and less detrimental than shock collars. They work by spraying a burst of citronella or lemon scent at the dogs nose. This not only is more effective at stopping the dog, it may distract him long enough for you to regain control or for the cat to get away. These collars are more pricey than shock collars, but they are safer and typically much more effective. You should also consider walking him in a headcollar instead if a regular collar, chain, prong collar, or harness. Headcollars give you much more control of the dog and above all they give you control of his head. If he can't make eye contact with a moving object, he will be less likely to get so amped up about it. Use whichever headcollar works for you, there are a few different styles available at pet stores. They also take about 2 weeks for the dog to get used to, so it's normal for them to throw tantrums on walks for the first few times they wear it.
    For now avoid any situations where the dog can get out. When company comes over, put the dog in the yard or in another room behind a closed door so he can't get past the door. Don't take any chances whatsoever, so that you avoid those "when we least expect it" moments. This will be an inconvenience, but much less inconvenient than being sued because your dog got the neighbors cat. Again, I cannot stress enough the need to hire a professional to evaluate your situation. Only they can evaluate the full extent of the dog's behavior and help you manage it. I hope I was able to help a little, best wishes to you and your dog.