Allergies, including food allergies, household dust, and seasonal allergies to pollen or mold spores may be a cause of picking in some birds. Food allergies may also be a significant factor. I personally question the use of some food additives, particularly artificial food coloring, in the manufacture of pelleted diets and won't feed them to my birds. Some birds may have negative physical reactions to components in other foods and dietary supplements. It is however, difficult to pinpoint the exact cause of food related allergies.
Airborne pollutants can also be a problem.
It is not natural for parrots to be confined to a situation where they have to breathe the residue of their droppings, food waste, or feather dust. Household pollutants of many kinds may play a significant role in feather picking problems. Cigarette smoke can be particularly damaging to a bird's sensitive respiratory system and physical contact with nicotine on an owner's fingers or hands can cause serious skin reactions. Problems caused by cigarettes due to breathing the toxic smoke, filthy feathers and physical nicotine contact reactions, could be a major factor in many cases of skin and feather problems. Any physical injury is likely to cause a bird to bother its feathers in the area of the trauma.