Most birds don't actively attack people though and only bite in self defense. Female parrots bite more and harder than males because they have to defend the nest.
Some parrots will bite and there was a corella (white cockatoo) at a pet shop that we used to sell angora rabbits to. The bird had a thing about toes and would jump off its cage and bite people's toes. It went me every time we went to the shop because I wore thongs (flip flops for the Americans) on my feet.
We had a corella in the shop I worked at (different shop to the one above) and she was a lovely bird. Never bit anyone, used to say hello to everyone when they came in and goodbye when they left. People could pat her and scratch her head. One day this kid was walking past her cage and he had a balloon. The bird reached out with its foot and popped the balloon. The bird was screaming, the kid was screaming, dogs started barking, people were running around wondering what just exploded. The poor bird was hanging upside down on its perch freaking out while the kid ran around the shop screaming because his balloon got popped.