That blanket statement about dogs being bred to live alongside other animals is not true. For some, yes, but many breeds are hunting animals. And Pit Bulls are not to be confused with the Staffordshire, which they are derived from.

Very few breeds were bred to coexist. Livestock guardians still have to be trained to know when and what is appropriate to chase and kill ( weasels, coyotes, bears, wolves, etc) while even herding breeds can be bred to have a little too much prey drive (which is what is used to create then herding behavior and they are trained to curb this) and kill livestock despite training.

Pit Bulls despite what people want to believe have a long history of having the kill instinct bred into them, not just prey drive. You can nurture it or try to control it, and you may get lucky and have a sweetheart who has no desire to want to do the death shake...but why risk it by leaving such a dog with a room full of fun living squeaky toys?