A psycho that you hate, or a person that bugs you all the time. You call them a crayon-eating parrot because they are weird and they even LOOK LIKE A PARROT!
Imagine you are out on a field or tarmac and, suddenly, someone hits you in the face with a dodgeball and they say, "watch out kid. you had it coming." You would say, "oh my gosh. what a crayon-eating parrot! geez!"