Why is it a sin to kill a mockingbird?

This is because mockingbirds merely bring beauty and happiness into the world. At one point Miss. Maudie explains,

"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 mocking bird."

The title refers to innocent people like Tom Robinson and Boo Radley who, like the mockingbird, only wish to bring a little happiness into a harsh world. For their efforts they are chastised, shut away and, in Tom's case, killed.