Atticus tells his children that it is a sin to shoot mockingbirds. His statement surprises Scout so much that she asks Miss Maudie about it. Miss Maudie agrees with Atticus, explaining that mockingbirds are harmless creatures whose sole existence is to add joy to everyone's lives.
“Mockingbirds don’t do one thing but make music for us to enjoy. They don’t eat up people’s gardens, don’t nest in corncribs, they don’t do one thing but sing their hearts out for us. That’s why it’s a sin to kill a mockingbird."
In the story, mockingbirds are a symbol of innocence and goodness. When Tom Robinson is shot to death, Mr. B.B. Underwood, the owner and editor of the Maycomb Tribune, 'likened Tom's death to the senseless slaughter of songbirds.' Tom represents a mockingbird which has been cut down mercilessly despite its innocence. In court, Tom's kindness and solicitude toward Mayella is unscrupulously framed in a negative light by the prosecution.
Later on in the story, Mr. Tate, the Maycomb County sheriff, refuses to hold Boo Radley responsible for killing Bob Ewell. He tells Atticus:
"To my way of thinkin’, Mr. Finch, taking the one man who’s done you and this town a great service an‘ draggin’ him with his shy ways into the limelight—to me, that’s a sin. It’s a sin and I’m not about to have it on my head. If it was any other man, it’d be different. But not this man, Mr. Finch."
Mr. Tate asserts that Boo has essentially made sure that justice was served in the town of Maycomb:
"There's a black boy dead for no reason and the man responsible for it's dead. Let the dead bury the dead this time, Mr. Finch."
Therefore, to drag Boo Radley out into the limelight for the act of protecting two defenseless children would be like 'shootin' a mockingbird...'