Hope this link below helps you on why birds bite....
I have a cockatiel and she's the best cause she hasn't bitten me at all. I guess the owners who had her were very good trainers or it's just in her nature.
Before though, I had some cockatiels that did bite and broke the skin. They have attitudes and feelings to in my opinion. Every bird is different with each individual.
Good luck on understanding your pet. These guys, the cockatoos are quite the characters as I have seen them online on YouTube and they are funny.