How did Scout and Jem learn about the sin of killing a mockingbird and how did their lesson relate to Tom, Arthur, or both?

Uncle Jack bought Scout and Jem air rifles. In this context, Atticus gave them a stern warning. He stated that they could shoot at all the bluejays they wanted, but they should never shoot a mockingbird. To do so would be a sin.  In fact, these words are so memorable that Scout remembers that this was the first time Atticus called something a sin.  Here is the quote:

Atticus said to Jem one day, “I’d rather you shot at tin cans in the back yard, but I know you’ll go after birds. Shoot all the bluejays 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.

As the story progresses, both Scout and Jem are able to relate this concept to life.  It is a sin to kill a mockingbird, because all they do is good things.  Therefore, it is a sin to harm anyone who only does good.  Tom Robinson is an example.  So, when Maycomb hurt him, Maycomb killed a mockingbird.  Boo is also a mockingbird.  All through the story, he only did good things for the children. Therefore, it is imperative to protect him.