It must be a really tough position to be in, and not one that many would understand.

Whilst it's true that any dog can attack and cause serious injury, some breeds have been specifically bred for aggression and traits that make them good fighting/hunting dogs. These same traits mean that they generally do not make good family pets - there are exceptions to every rule, but for the most part the dog has a deeply ingrained instinct that is difficult to overcome. Most dogs when provoked to the point of biting will snap then release. Enough to get the result they're after, the cessation of whatever behaviour is distressing the dog.

Some breeds though, do not release - and a pitbull is one of these. They will keep going. And going. And it's that that causes the severity of the injuries seen. Personally, that's not a risk I'd be willing to accept around young children. Simply because no matter how much supervision there is, and how well trained the dog, there is always the risk of a kid finding that one thing that triggers an aggressive response.
Exactly what I would have written. It's a really tough situation to be in. While a dog's upbringing certainly plays a huge role in their demeanor and personality, there are still always inbred traits that are carried in the blood lines. Just look at Chihuahua's who are notorious for being very snappy. But would you prefer a Chihuahua snapping at your face, or a pitbull?

Before having kids the majority of my "professional" career was spent as a surgical vet nurse. I've experienced pretty much every breed you could think of over the many years. I also run puppy classes for a number of years so experienced these breeds as both puppies and adults. I generally don't have a "fear" of any particular breeds, but I am certainly more wary and careful with some. Those include Pitbulls, Kelpies, Malamutes, GSD's, and some cattle dog breeds (Heelers and Border Collies). Sure, I've seen some absolutely beautiful dogs of those breeds, but in my experience those have been some of the breeds we've seen the most behavioural problems with. Strangely, for a breed that can often be confused by many people as Pitbulls, I've never once seen a nasty Staffy.

Animals around kids can definitely be tricky. When ever I was asked "what breed dog should I get for my kids?" my general answer was a Cavalier King Charles Spaniel if they could afford the possible heart complications the dog was likely to have, lol.