He doesn't want to. But through out the book there are clues that he comes out. Like when Miss. Maudie's house was on fire, Jem and Scout went across the street in front of the Radley's house. When the fire was out Scout had a brown blanket draped over her shoulders, only Boo could have put the blanket on her because Nathen (Boo's older brother) was across the street helping put the fire out and getting Miss. Maudie's stuff out of the house. Also when Scout and Jem would walk by the tree in front of the yard they would find things that only Boo would be able to put in there. And in the end of the book Boo helps Jem and Scout. He only comes out when he feels like he needs to is basically the answer.
Arthur Radley, also known as Boo, stays in his house because his brother, Nathan forces him. Boo got into trouble with the law when he was young so his father made him stay in the house for 15 years. After his father's death, Nathan moves in and continues the isolation.
Dill believes that Boo Radley has not run away from his home because he is not crazy, but simply chooses to stay inside to avoid the cruel world outside. Dill thinks that Boo stays to protect those he cares about.
Arthur Radley stays inside the house because of his reclusive nature and the rumors and stories spread about him by the townspeople. He is portrayed as a mysterious and misunderstood character in "To Kill a Mockingbird," leading him to isolate himself from society.
Boo Radley saved them from Bob Ewell when they were walking home form Miss Maudie's play, because Bob Ewell broke Jem's ankle and Boo Radley cam to the rescue and carried Jem home and Scout was right behind them.
They are probably attached to that room for whatever reason.
Arthur (Boo) Radley is the son of the Radleys in To Kill A Mockingbird. He stays in the house.
Jem realizes that Boo Radley is kind and a protector when he leaves gifts for him and Scout in the knothole of a tree. He understands that Boo has been watching over them, showing that he cares for their well-being. Jem's perception of Boo changes from fear to compassion and gratitude.
Jem was convinced that Mr. Radley kept Boo chained to the bed most of the time, but Atticus said no, there are other ways of making people into ghosts (he didn't elaborate as to what those ways may be).
In the last few pages of the book, after she walks him home and she stays there and reflects on his history with them.
The first time he stays the night at kagomes house is in episode 82
The quote is "Scout, I think I'm beginning to understand something. I think I'm beginning to understand why Boo Radley's stayed shut up in the house all THIS time. It's because he wants to stay inside."
Stays in the Mass state house!