Certain breeds have been bred for certain traits, just as they have been bred for a standard appearance. Unfortunately, when a breed becomes extremely popular quickly, careful breeding is often a casualty. Physical faults, such as hip dysplasia, skin allergies, etc., start manifesting, as do undesirable personality traits. Sometimes the less desirable traits become more pronounced as unethical breeders inbreed their existing lines. Sometimes people will even breed purposefully for aggression. How many times have you heard someone talk about how well their dog fights, or how aggressive it is? Or how many cats it has killed?
Also, a dog owner should be responsible; be realistic as to whether or not you can really handle the breed of dog you are interested in, socialize your dog, teach your dog what is acceptable behavior and what is not, assess whether or not your home is appropriate for the breed. Remember, a bored or frustrated dog is going to take it out on something. It may be your shoes, or it could be your neighbor's cat, dog - or your neighbor. You should also take into consideration what kind of neighbors you have and how well they control themselves, their children and their pets. You may have to make an effort to make sure your dog is not being teased or tormented by the idiot next door! Privacy fences can be your dog's best protection.
And be aware of what kind of signals you are giving your dog. They try to do what we want them to do, and are often very sensitive to our emotions. Your dog will try to protect you; if you feel threatened or an intense dislike for someone, chances are your dog will feel it. If you're angry and aggressive, your dog is going to pick up on that - and potentially act on it.
I had a friend who raised chows. When she had her little girl, I was a little concerned, although her dogs had always been very sweet and docile. I didn't need to worry. When her baby started walking, she learned to pull herself up and walk hanging on to the dogs. They were always gentle, walking slowly and encouraging the baby to take her steps, stopping to nuzzle her when she fell down. I wouldn't have given very good odds to anyone who tried to hurt that baby, though!