dog bites man again and again

Either the dog or the leg are artificial. Maybe both.

Are aggressive pit bulls and other breeds of dogs inherently violent, or are they made so by their owners?

It is both nature and nurture, of course. 

However, let's consider different species. How many people are bitten by rabbits? By goats? By guinea pigs? Probably not too many, nor too seriously. Could you provoke a rabbit to bite you? Yes, but it would take persistence. 

The point is that animals exist on a continuum, from shy to scary. Sharks, rattlesnakes, and alligators are considered dangerous. Some sharks are more mellow than others, but all in all, they're at the dangerous end of the spectrum. 

Clearly, so are dogs. Humans started out with wolves and domesticated them into dogs. In fact, the modern canine is largely a human invention. Dogs were bred to guard, attack, hunt, and bite. Certain species were intentionally bred to have strong jaws and the capacity to maul. 

There are many types of dogs now, but as a group they're closer to the shark end of the line than the bunny end.  Face it. Snails, turtles, bats, woodchucks, beavers, or otters are highly unlikely to bite you. 

Most dogs will not bite you.  A lot of them will. 

 According to the U.S. Centers for Disease Control and Prevention, "about 4.5 million people are bitten by dogs each year. Almost one in five of those who are bitten;  (and) a total of 885,000: require medical attention for dog bite-related injuries. In 2006, more than 31,000 people underwent reconstructive surgery as a result of being bitten by dogs."

The  "dog bite denial" folks point out that there is no way to determine which breeds are more likely to bite you. True. But obviously, pit bulls put more people in the hospital than beagles. There is a reason that German shepherds are the dogs of choice for protection and paramilitary work. 

For mysterious reasons, people these days tend to be more concerned about animal,  rather than human, welfare. (It's possible to care about both). This society sends people who hurt dogs to prison. 

What we don't do is hold hold owners accountable for their dogs.  Only in the most serious  mauling cases are the dogs themselves killed, or are people charged with a crime.  

Dogs can be a gentle, loyal,  lovable part of a family. They can provide nonjudgmental companionship. But owners need to control their dogs as if each pet is a potential killer.

 Especially people who insist on owning pit bulls.