To Kill a Mockingbird is all about mockingbirds, even though the actual word is only mentioned three or four times in the novel. The reason it's a sin to kill a mockingbird is because
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.
Boo has never done anything but try to be kind to the Finch children; he minds his own business and helps when he can; his only sin was being born different. Tom has never done anything but be kind and helpful to a young woman who clearly needed help; his only sin was taking pity on a white woman.
Atticus is not an obvious mockingbird, as he is neither poor nor black nor an outcast. Instead, his offense is trying to do the right thing in the face of prejudice and hate. For trying to right a wrong--"to make music for us to enjoy"--he was spit on and villified, and his children were nearly killed. That makes him a mockingbird.
Atticus most definitely could be a mockingbird. This bird is nondescript in coloration and yet can imitate or sing many different bird songs. Atticus is not a spectacular looking man, nor does he have any outstanding traits (according to his children) that would set him apart from other dads. Yet he hides the unpleasantness of the world couched in neutral terms when his children ask those difficult questions about life in Maycomb. He does not raise his voice, like a loud crow would. Nor does he scold like a blue jay. In court, his statements are neutral in tone and phrased to fit the mentality of the witness and jury. His bravery and courage was always understated, just as the mockingbird's appearance is. Until he opened his mouth and wisdom poured forth, no one would find him remarkable, just like the grey mockingbird.