Dog aggression in the pit bull is something very misunderstood by people unfamiliar with typically dog-aggressive breeds. Dog aggression is not, per se, a bad thing. It does not in any way make the dog a bad dog. It is simply a part of the temperament, and an aspect of the breed which needs to be recognized for what it is and managed in a responsible manner.
Pit bulls-- and here I lump together both the American Pit Bull Terrier (UKC) and the American Staffordshire Terrier (AKC) because they are, in my eyes, the same breed-- were developed originally for bull and bear baiting. When this "sport" was outlawed, they were moved into the dog fighting pit. They were bred for generations, and, unfortunately still are, to be aggressive toward other dogs, and to be strong enough, determined enough, and to have the stamina to fight to the death, either their death or that of the other dog. All of these characteristics are often lumped together under the term "game" (ie the "game-bred pit bull"). Because of their history in the pit, they were selectively bred for these characteristics. This is no different than how other working and sporting breeds were developed- dogs who excelled in their jobs were allowed to reproduce. This is how pit bulls became the breed that we have today.
Dog aggression has a full spectrum, like any other characteristic. There are pit bulls who get along with every other dog they see and can go their entire lives never showing aggression. There are pit bulls who are off-the-wall aggressive toward every other dog they see and cannot safely be allowed around other dogs. The vast majority fall somewhere in the middle, however most pit bulls do have some propensity for inter-dog aggression. They may not actively aggress, however if challenged, they will also not back down. Because of their body type, drive, and determination, most pit bulls if challenged by another breed, will win a fight.
It is not possible to socialize dog-aggression out of the pit bull. A pit bull can be very well socialized as a pup and still reach sexual maturity and become aggressive toward other dogs. This is often referred to as "turning on". Pit bulls do not fight other dogs because they are insecure around them or fearful of them. They fight other dogs because it is instinct. It is what they were bred to do. It is the same as a Border Collie's instinct to herd or a Labrador Retriever's instinct to retrieve. We do not expect to be able to socialize out those characteristics from those breeds, do we? It is no different with dog-aggression in the pit bull.
This is not to say that socialization of pups is not necessary, or that dog-dog aggression cannot be controlled, or that pit bulls should never be allowed to be around other dogs. Socialization as a pup is just as important, perhaps even moreso, as with any other breed. Pit bulls need to learn to behave appropriately with other dogs just as much as the rest of the dog population. However, it is dangerous to fall into the trap of thinking that because the pit bull interacts well with other dogs as a pup, it will always do so. Obedience training is also important. There is no reason a pit bull should not be able to control itself on leash around other dogs. That is a training matter. No matter how badly a dog wants to do something, it can be trained not to in a controlled environment. But training is not going to take away the instinct or the desire to fight.
What does this mean? It means never trust your pit bull not to fight. It means never leave a pit bull alone with another dog. It means that allowing a pit bull to run in an uncontrolled environment with other unfamiliar dogs is irresponsible and an accident waiting to happen. What does this not mean? It does not mean that a pit bull should ever show aggression toward humans. Human aggression and dog aggression are absolutely different things (do we look at a hound who would happily kill a small fuzzy in the backyard and fear for our children? Of course not. Dogs know the difference between dogs and humans. It is humans who seem to have the problem with that). It does not mean that most pit bulls need to be socially isolated- many pit bulls enjoy playing with familiar dogs in controlled environments.
Another caveat to this issue is the increasing trend toward breed specific legislation (or BSL). Pit bulls are being banned from cities, states, and even entire countries all over this world. They are the center of a media frenzy right now, fed by the "if it bleeds it leads" mindset. If a pit bull is involved in an incident, you can be sure it will make the news. If it's a Lab involved, chances are it will either be called a pit bull or never make the news at all. People don't want to hear about "good old-fashioned family dogs" who get into trouble, but those pit bulls, they're downright dangerous. If a pit bull gets in trouble in a dog park, whether the pit bull started it or not (and in some cases, the pit bull wasn't even involved!), they will be on the news, and in some cases, this is enough to spark the start of legislation to ban them outright.
The key to all of this is responsible ownership. Pit bulls are a lot of dog to handle, and they are not the breed for everyone. But they do not need to be- that's why there are over a hundred breeds for people to chose from! Pit bulls need to be closely supervised and watched around other dogs. Owners need to know their dogs, and be aware of subtle signs of aggression that could lead to a problem. These dogs need training and consistant leadership. They are wonderful dogs in their own right, but they are what they are, and as owners we need to accept that dog-aggression is part of what makes them pit bulls.