Each bird is different. My parrotlet really likes being in his cage ("his safe place"; his territory) but he can easily and happily spend the entire day outside on the top of the cage playing with his toys. If his favorite play-thing is in the cage, he will probably stay inside even with the door wide open. If I place his favorite toy atop his cage, he follows it outside to the cage top. And he has no desire to fly around or wander, unless frightened. He is timid in that regard -- but many birds are more curious. Leaving the cage ..... is not really a learned response in and of itself.
What IS learned is him/her being trained to trust you. Once he trusts you, he will sit on your finger as you bring him slowly out from the cage. Or you can bribe him out with toys or food he likes by placing them outside the cage. But if the bird's wings are clipped, there is no rush to bring him outside the cage as he may end up crashing in to objects, walls, etc., especially if frightened.
Another aspect to consider is if the bird is new to your home. It is not unusual for a new bird to stay generally in the middle of the cage (safest place) for a day or sometimes for a few days, as they become familiar with their new environment. Everything may scare them at first -- new and sometimes startling "people sounds" they must become accustomed to; sounds of things like dishwashers and garbage disposals running, clanking of dishes; the sounds from a TV, etc. A bird may eat very little during those first few days of initial adjustment.
The main point here is to work with your friend, train and assure him he is safe ... and he will come out in due time -- when he is ready. But no need to force him out; you must feel out his character, emotions and let him set the pace.
