The horses live on protected federal land, and the horses themselves are protected wildlife. The federal hunt and slaughter is a cull to keep their numbers in check so they don't devastate the landscape eating every last bit of vegetation and then all starve to death. They want some horses to live there safely and happily. They just can't let all of them live. The horses don't have any natural predators because wolves have been extirpated from most of the US.