why is it a "sin to kill a mockingbird"?

The mockingbird represents a sense of innocence. It merely sings and brings joy to people.

You can check out the quote here,

"Atticus said to Jem one day, 'I'd rather you shoot at tin cans in the back yard, but I know you'll go after birds. Shoot all the blue jays you want, if you can hit 'em, but remember it's a sin to kill a mockingbird.'

That was the only time I ever heard Atticus say it was a sin to do something, and I asked Miss Maudie about it.

'Your father's right,' she said. '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.'"

The mockingbird also comes to represent innocents like Boo Radley and Tom Robinson.

The deeper reason is because mockingbirds are Confederate gray and blue jays are Yankee blue. (BTW, mockingbirds do eat up people's gardens. They peck my tomatoes, ruining them. Mockingbirds also drive bluebirds out of the bluebirds' nests. They are not some sweet, romantic southern thing. They are nasty bullies. Live with a glut of them year 'round, year in and year out and you'll see. You'll also see the bird diversity in your neighorhood go down. Besides singing, they make some nasty fussing sounds over and over and over)

What is Mrs. Dubose’s affliction?