I am a bit confused about this. So my parrot never bites (while in the cage), and I can (yes CAN) touch him. Here's where it doesn't make sense: before I touch him he always squaks for a few seconds but stops. But the big issue is that when he is out of the cage, he is unmanageable and screams and bites and won't let anyone near him.
I think he is not getting enough out of cage time. When he is out he is afraid that you are going to put him back in his cage. When he is out ignore him. Be with him without making one on one contact. Do not feed him out of cage. He should go back in when he is hungry.
Myrtle is so afraid of being caged that she will not go into the cage for food but just go hungry and thirsty. The above method does not work with her. She is so fearful even after being free for 6 years that she will not go into a cage that has a door.
This is just what I would do and others will give you more info.
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