There are facts about dogs everyone should .earn, many of them based on the breed and exhibited behavior.
A Pit Bull is not only the most dangerous due to their physical and innate ability to latch onto a victim (animal or human) and refuse to let go, but also because they have a tendency to not bark before attacking. They are fixated on the target, and barking is meant to warn off anyone they might feel threatened by. Once they attack, they keep attacking until restrained or the prey is dead. it's really hard to defend against that, so use of a weapon -- any weapon -- to defend yourself is recommended.
Large dogs like German Shepherds and Rottweilers are excellent attack dogs because of their size and weight. It's difficult to fight off an 80+ lb dog (my GSD averages about 85-90 lbs). Luckily, these breeds, unless trained as attack dogs, are mostly territorial. They don't often attack when not at their home. They'll bark, which gives the person being barked at time to be alerted and possibly find cover or otherwise react. If you watch COPS or any show that uses trained dogs for their security work, the dogs whine and bark when they see an adversary. But, as soon as the dog is released and ordered to attack, you don't hear any barking at all. Bottom line -- a barking dog is normally a dog not about to attack.
Any dog can cause injuries, but if the muzzle is too small to enclose your wrist, chances are the bite will not be more than superficial. That's not a deadly threat.
Having said that, if you're being accosted by a pack of dogs (3 or more), you have to consider the pack mentality. If one attacks, all will probably attack.
These are not rules, but they can be used as guidelines to justify the use of lethal force over waiting to see if the attack happens. Simply saying "I was afraid for my life" should not be accepted if the dog was incapable of posing a deadly threat. Fear of just being bitten should not be a reason to kill it.
Dogs are considered property, no matter how much we might think of them as members of the family. This dog that was killed is only worth what the owners paid for him or must pay to replace him. Had the dog survived long enough to receive emergency treatment, those vet bills can be claimed in a lawsuit as well. Beyond that, taking that life is not considered a crime. This becomes a civil matter over the monetary value of the property destroyed.
One thing that bothers me is the Cops who shoot dogs saying "I was in fear for my life." FEAR is what everyone is taught to NOT display when a dog is barking at you. Showing fear only emboldens them. Walking away slowly, while facing the dog, usually prevents escalation.
I understand if a Cop is on the job, they can't be slowed down or distracted from human threats by a barking dog. But, ending the dog's life should be the exception, not the rule.