The quote refers back to what Scout and Jem were told when they got air rifles for Christmas, not to shoot a mockingbird. A mockingbird doesn't do anything but sing many bird songs and harms no one. It isn't a predator or harmful to anyone. Tom Robinson and Boo Radley were symbolic of mockingbirds. Both men did nothing to harm anyone and were friendly to those in need. Boo was rumored to have stabbed his father in the leg with scissors in his younger years. Since then, he has done no harm, merely helped the children the night of the fire and given them little presents in the knothole. Tom was the only human being who was pleasant and helpful to Mayella Ewell. Their kindliness and helpfulness without expectations of return made them the mockingbirds of Maycomb.