I'm not really sure if you're referring to naturally wild pets that have been 'tamed' or domesticated pets that go wrong. The first is obvious, most people don't realize that domesticating an animal takes generations. The dog for example has gone through about ten thousand years and cats a couple thousand less that that. You can easily compare the two and see the difference in the level of domestication. So when you just take a wild animal out of it's natural habitat, it's always foolish and even cruel to stick it into a cage and call it a pet. Ultimately that's the core problem in Blackfish because orcas aren't domesticated animals for our entertainment but wild predators we've stuck in essentially a bathtub for thirty years and Sea World has biologist and expensive equipment to keep the orcas healthy. How can some layman have wild animal and hope to keep it safe and healthy for a long period. Of course it's only natural that it would turn on it's caretaker.
Then you have to take in all the cases where the pets go wrong. Any animal that has been abused long enough is going to bite, kick, and defend itself once it reaches it's breaking point. That's to be expected and unfortunately some people get pets who've been abused and don't know it or underestimate the psychological problems. Those animals are to be pitied of course, they didn't ask to be abuse, but you need to on guard and experienced with dealing with the animals's problems not only for you safety but for theirs. Though I do think some of the trouble that can occur, especially with dogs, is that people pick based on looks instead of doing proper research based on temperament. There is a whole section of dogs that should be considered exclusively work dogs and don't have the temperament or mentality to just be a house pet. One of the meanest dogs I ever met was a Doberman Pincher that my friend kept in her apartment as a pet. I don't actually think they are a mean breed by default but they're highly intelligent and need to work to keep from being bored. Her boyfriend adopted the dog and took it with him hunting. While that wasn't the original purpose, the exercise and the discipline her boyfriend gave it softened the temperament over time. The work actually made it a better house dog in a weird way. So some dogs just aren't meant to be cooped up in a house all day while you work, they want to work to. Plus, if you have kids most of their squealing will set off the hunting or herding instincts of the older work dog breeds. This isn't always horrible. My grandma's friend had a collie that was trained to herd the grandkids past a certain point to ensure they don't escape into the pasture and get bit by a rattlesnake. I think between abuse and just having the wrong dog for the wrong household will always lead to problems.