Breed really matters. It's obvious really - breeding is done to promote very specific behaviours and characteristics and it works.
I've had a number of breeds of dog over the years and the difference between them has been marked. In particular, a terrier we had was entirely focussed on killing small things, when out of the house, and would be liable to attack anything intruding into her personal space, or any Boxer dog within 100 yards. In the training venue she would be a model dog and easily passed the Kennel Club Gold award, but once out on a field she wouldn't even make eye contact, being solely focussed on hunting. If let off the lead she would end up rampaging through gardens in search of rabbits, so we weren't able to let her off the lead outdoors with any confidence until she was fifteen. Yes, if we'd spent (even more) countless hours training her for years, it might have made a difference, but she really was verging on being untrainable in some ways - little interest in food and very single minded. Luckily, she was effectively a long-legged Jack Russell so was not a threat to life and limb, and she was very tolerant of the cats at home. The cross Lab we had, on the other hand, was entirely agreeable, eager to please, and was never aggressive to anything.
Put the wrong breed of dog with the wrong type of owner and there will be trouble. Bully-breed dogs are capable of devastating attacks and yet seem to attract people with little concept of how to handle them safely and with little regard for the safety of others.
What can be done about it? Very little.
