If the dog had been a person, and identified by the courts as a convicted person on probation, which is sort of what the dog was, and this person was running at the man and his child, would there be this many comments against the shooting?  I doubt it. 
Had a sign been posted, "Dangerous Dog" on the lawn, would the gentleman have parked there knowing he would be possibly putting his child in danger?  Probably not.
Sad a pet, a member of a family died in this way, and traumatic.
If I am in the same situation, I probably do the same thing, but it is difficult to know until placed in the same situation.  No animals life is worth a a person, or injuries to the person if they have acted appropriately, and it does not sound like this gentleman was antagonizing this dog.