All breeds and all mongrels belong to one species of dogs – domestic dogs. If dog is a dog, if American Pit Bull Terrier is a breed and not a separate species of dogs, if any Mastiff is a breed and not a separate species of dogs, or any other dog with unnatural tendencies, there is not one reason to avoid spaying and neutering to prevent further reproduction of these dogs. If this is a way to deal with problem of stray dogs (and it is ok), why not do the same with breeds that carry unnatural fighting gene.
It would not be the first time in history that one breed of the dog vanishes. Some Mastiffs and Terriers no longer exist. The reason for it is unknown. Maybe by killing, but that is absolutely unacceptable. The only appropriate, although long lasting process for solving problem of the existence of these breeds is CNR (Catch–Neuter–Release) method, only bringing the dog home instead of putting it back on the street.
Old English Bulldog is an example of extinct breed. It originated in Britain. It was used in bull fighting. It weighed around 20 kg. It was mixed during creation of many other blood sport breeds such as Bull and Terrier, breed that also does not exist anymore and was also created in Britain, which is predecessor of American Pit Bull Terrier, Staffordshire Bull Terrier, American Staffordshire Terrier and Bull Terrier.
Cordoba Fighting Dog is a breed that also does not exist anymore. Its origin was in Argentina. It was used in dog fighting. It had high pain tolerance and great appetite for fighting till death. It was usual for it to rather slaughter a female than mate with it during breeding. It is immediate predecessor of Dogo Argentino.
Dogo Cubano is a Mastiff. Extinct breed. It was used for dog fighting and capturing runaway slaves. After abolition of slavery they ceased to exist.
Reasons why dangerous dogs exist
There is no reasoning. If they were made to fight – they should not exist, because this way they are an object of abuse, if they were made to hunt wild animals – they should not exist since wildlife is endangered and they should not be hunted. Humans started with domestication of wild animals around ten thousand years ago with aim to help with food gathering. Wild animals have a role in ecosystem and if humans stopped with taming of the nature, as well as killing wild species for sport, fun, prestige... nature would regulate number of specimens of all species in order to keep the food chain sound.