Verbal irony exists when the spoken words of a person or character convey a meaning that is contradictory to the actual, literal meaning. Often, this is done with the hope that the listener will note the irony of the statement.
In chapter 16, Aunt Alexandra is once again trying to give Atticus advice on how to manage his household. First, she tells him that he shouldn't talk so openly about Braxton Underwood's racism in front of Calpurnia. Atticus dismisses her, saying that anything they talk about in their home can be openly shared with Calpurnia because she knows how important she is to the Finch family. Then Aunt Alexandra listens as Jem tries to process the lynch mob from the previous evening. He can't believe that Walter Cunningham was in the crowd. Atticus tries to explain how even generally good people have "blind spots," particularly when they become part of a mob. Aunt Alexandra doesn't like the children hanging around with the Cunninghams, believing that the Finch family shouldn't associate with such "low-class" people. Scout swears that the next time she sees Walter, she's going to exact a revenge for his father's participation in the lynch mob, and Atticus quickly tells her that she will do no such thing.
At this point, Aunt Alexandra interjects again, telling Atticus,
You see, don’t you ... what comes of things like this. Don’t say I haven’t told you.
Atticus's response is an example of verbal irony. He tells Aunt Alexandra that "he'd never say that." On the surface, it sounds like he's agreeing with her. But in actuality, Atticus means that he will never tell Aunt Alexandra that she has "told him" better because he so strongly disagrees with her position, which is evident in the way they disagree on various matters during this conversation. Of course, he's hoping that she picks up on his ironic comment.