As Mocking Birds do nothing but sing and Tom Robinson did nothing he was just a innocent person. Hence the quote 'It's a sin to kill a mocking bird' as mocking bird cause no harm and neither did Tom Robinson. Hope this helps.
Primarily the mockingbird is a symbol of innocence and is used as a metaphor for the innocent yet victimised Tom. The book states through the words of Atticus that “it is a sin to kill a mockingbird” i.e. it is a sin to kill something or in this case someone that has done nothing wrong.