This is exactly why we shoot any dog that comes on our property. When we get new neighbors we warn them, some listen, some learn the hard way, (our state law actually states that it is our responsibility to shoot strays). It isn't just pitbulls, all dogs that are allowed to roam are subject to the pack mentality. If you had ever seen a baby calf or a colt half-eaten alive you'd understand.
Glad you aren't our neighbor. Shooting any dog on sight is definately on the paranoid side, most dogs do not become instant killers when loose. We don't allow our dogs to roam, but we have one that will run if he gets an opening and we aren't home, despite our best efforts. He's not hunting, he's looking for us. We worry about him endlessly till some kind soul finds his phone number on his collar and calls, sometimes miles away. There's a difference between people who make no attempt to control their dogs, even those known to be dangerous, and pets that can sometimes get out purely by accident. Ours is no risk to stock or pets or children and even a moderately astute eye would see that. Please don't shoot without discrimination.