I realize defenders of certain breeds engage in a form of quasi-creationism where all breeds have the same tendencies, but there's no way you actually believe that all animals are the same, right?
We breed animals to favor certain characteristics, it's an inherent part of selective breeding. It's the reason why my Golden Retriever likes carrying things in her mouth 24/7, it's certainly not a learned behavior.
Wait, what? You want to wipe out an every pit bull/shar pei mix? What the fuck will that do exactly?
The moron's solution... people will just keep another breed, untrained... and yield the same results. Then people would be crying to, for example, "kill all labradors!".
Some dog breeds will instinctively protect your live stock, and other dog breeds will instinctively eat your live stock. Neither has to be trained or abused to cause this.