Why does Atticus decide to keep the blanket incident a secret in To Kill a Mockingbird?
After the children and Atticus return from the fire that consumes Miss Maudie's house, Atticus notices that Scout is wearing a blanket around her shoulders. When he inquires about its origin, Scout answers, "I don't know,sir...I--" She, then, turns to Jem, who is even more puzzled than she. But, Jem "babbles," and reveals the entire history of their doings at the Radley house including the placing of items in the hole of the Radley tree. Jem informs Atticus,
'Mr. Nathan put cement in that tree, Atticus, an' he did it to stop us finding things--he's crazy, I reckon, like they say....'
It is with this disclosure that Atticus changes his mind about returning the blanket to Boo, for he realizes that doing so may bring repercussions onto Boo as Mr. Radley would know that Boo has continued contact with the children, an act which he means to halt by already having stopped up the tree hole.
Following Miss Maudie's house fire, Atticus notices that Scout is wearing a blanket on her shoulders. When Atticus asks where she got the blanket, both Scout and Jem seem puzzled. Atticus then smiles and implies that Boo Radley gave Scout the blanket. Jem immediately panics and begins telling his father about their "secret" interactions with Boo. Atticus then calms Jem down and suggests that it would be best to keep the blanket instead of returning it. Atticus is probably aware that Nathan Radley will chastise or threaten Boo for leaving their home and giving the blanket to Scout. Nathan has already plugged the knothole in the oak tree to prevent Boo from communicating with the children and has more than likely warned Boo not to interact with Jem and Scout. Atticus is insightful enough to realize that returning the blanket will probably cause problems for Boo.
Atticus respects Boo Radley's privacy. He knows Boo did it and reveals it to the children, but he doesn't want Boo being brought out into the limelight. If you aren't already to the end of the book, you will learn in chapters 29-30 that Heck Tate will do the same thing for Boo.
Boo is a good character and you will find a moral hero in the story, but he's not the typical guy - he's a recluse or a hermit. Atticus respects Boo for his ways and encourages his children to do the same.