|We love our birds. We love looking at our birds. But some of us have birds that are unapproachable. If we put our hand in the cage, the bird backs up. He might not even try to bite you but doesn't want to be approached. The bird basically shift its body back when you try to approach it. It may just turn around and ignore you when you try to get it to come out of the cage.
First it's important to remember that although you might want to pet and cuddle your bird your bird just might not want to be pet and stroked. Sometimes have to strike a balance between physical touch and nonphysical interaction which could be talking or whistling, sharing food or even just being in the same room.
To make headway with any bird you have to respect their wishes and not force your desires upon them. If you're lucky enough to have other birds sometimes having the shy bird watch other birds play among themselves or play with the toys could be helpful. Many of us only have one parrot.
It's important you recognize your parrots daily routine. Do they notice their shadows is a sudden changes position in the sky? Does he start vocalizing at certain times of the day? Does he play with his toys and dances with in the cage? This could be a sign that your bird wants to play but does know how to play with you.
Food can be a common bond between the two of you. Something as simple as dropping a favored a treat into a food dish every time you walk by the cage can be helpful, while at the same time singing words of praise or just "hello"
It's best not to hang over your bird when a predator but just to be in the same room not even making eye contact, at least for a while. Eye contact can then be a good start. Blinking can even be a form of communication with your bird. Blinking can lead to a game of peekaboo where now you are interacting with your bird but not touching your bird.
Sometimes your bird may pretend to bite you or tug on your hair making you jump back or screech. Birds are very smart. This type of activity is so prevalent it has a name the "drama reward". Basically the bird learns they can be rewarded without even biting a human. You can use this to your advantage. A parrot who has learned the drama reward game may allow you to touch your bird by rewarding the bird with the rewarding sound of "ouch". In other words with your bird in its cage you could walk over to it, makes eye contact and then slowly reach towards one of its toes pretend to touch it. Ready for touching the toe jump away and scream "ouch". Guess what - you were just able to touch your bird with other negative reaction on their part. You can also try on different parts of the bird, the tail the head and so forth.
The key here is patience. Your bird is going to be on this planet for decades, spending a few days or weeks learning how to interact with your bird can yield rewards that will last a lifetime.