They would pin their eyes and become as threatening as possible. You become part of the problem not part of the solution. So he takes a swipe at you to get you to fly away so he can defend the territory and you can fly back when it is safe. If a parrot takes a jab at another parrot, he most likely gets a beak full of feathers. If he takes a jab at you, he gets a face full of skin.
Facial bites can be quite serious resulting is scarring and even eye injury.
Many people think they are the exception until they experience aggressive behavior when their parrot is on their shoulder. He can play happily and you can establish both friendly and disciplinary eye control with him. Don't turn it into a game with drama. Do this over and over until your arm is no longer his runway to your shoulder. Do not get into the habit of just leaning over to his cage and having him step on your shoulder.