Medical Reasons
I want to say first off that the most important thing you can do for a feather abusive parrot is to take it to the vet. There are many physical causes for feather abuse, and nothing you do behaviorally will change this abuse if your bird is sick. Some of the things you should have your companion tested for are :
Parasites, be sure your vet looks for internal as well as external ones.
Bacterial or Fungal infections
Malnutrition, even if you feed only the best you bird may not be getting what it needs.
Metabolic or Organic diseases
These are not the only things you should test for, but they are some of the most important. You should also have your vet look for any broken feathers in the area of the picking, sometimes its as simple as discomfort which became obsession. If your bird has gone as far as self mutilation you need to consider some painful options, such as a collar or in extremely severe cases, euthanasia. I'm not recommending that birds be put down, but I do believe that an animal who will never live a normal life without pain again needs to have that considered.
REMEMBER: Illness in pet birds can be extremely difficult to diagnose by physical exam alone as birds are notoriously capable of hiding symptoms!!! For this reason ALWAYS, regardless of history or physical exam findings obtain a minimal laboratory database to uncover any occult.."Hidden"... abnormalities. Often an x-ray is added to the database, if the owner is willing.
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Behavioral Reasons
There are many different things that can lead a bird to pick its own feathers. Boredom is a major reason for feather picking. Sexual frustrations is another. If your parrot has been medically cleared by your vet then its time to take a long hard look at your environment. What things should you change to help your bird stop picking? Sometimes its as easy as a small change, such as moving the cage to a lower traffic location. Look for new furniture in your home too, your parrot may be perceiving the new item as a threat. Is your bird highly stressed? Some species of parrots stress far more easily than others, you need to research what each individual species in your home needs.
Its also important to look at the amount of time you spend with your bird. Sometimes you may need to add more one on one time to your life with your bird, and in other cases you might have to cut down and allow your bird more alone time. Look at the quality of the time your bird spends with you. Do you sit with your parrot on your shoulder and watch T.V.? Some birds become bored and pick, you might want to initiate games with your bird.
Habitual feather abuse is the hardest to make any headway with. Parrots who pick habitually can be compared to a human who bites their nails. It serves no real purpose, but it is very hard to stop doing. However, it is possible to stop in most cases, with intensive time and work to help create better habitual behaviors to replace the problem one.
Any feather abuse should be looked into by a vet as soon as possible, to try and prevent it becoming habitual. We cannot stress enough how hard it is to break a parrot of habitual feather abuse, so the best method is to prevent it if at all possible.