In "To Kill a Mockingbird," Atticus tells Scout and Jem that it's a sin to kill a mockingbird because they are innocent creatures who do nothing but sing. The mockingbird is used as a symbol of innocence throughout the book, and its significance is explained by Miss Maudie when she says, "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." By killing a mockingbird, one is destroying something innocent and pure, just for the sake of doing it, which is a sin.
Moreover, the mockingbird symbol is applied to Tom Robinson, who is an innocent black man falsely accused of rape. Like the mockingbird, Tom Robinson is innocent and is only trying to help those around him, but he is ultimately destroyed by the racist society that he lives in. When Atticus says that it's a sin to kill a mockingbird, he is also referring to Tom Robinson's case, as he is an innocent victim who has been wrongfully accused and punished for crimes he did not commit.
In the book, the theme of protecting the innocent and vulnerable is a major one, and the mockingbird symbolizes this. It is a reminder that we should strive to protect those who are innocent and defenseless, rather than causing them harm. The book's title itself, "To Kill a Mockingbird," is a reference to this theme, as it emphasizes the importance of protecting the innocent from harm.