The humor of this Atticus Finch Lesson is just like the humor in most of Atticus' lessons. Instead of avoiding the situation, glossing over it, or simply ignoring it (as many parents do), Atticus tackles Scout's question in his own very straightforward and matter-of-fact way.
First, he tells Scout that "n*gger-lover" is basically a silly made up word used by ignorant people. In Scout's words (which Atticus accepts as a viable example) it is much the same as "snot-nose." Scout clarifies by asking, "You aren't really a n*gger-lover then, are you?" Atticus' response is probably key to the humor of this situation.
Atticus says, "I most certainly am. I do my best to love everybody..."
Instead of allowing the term to be the insult it was intended to be, Atticus takes the word at face value and agrees with it. The effect, therefore, is Atticus once again rising above the immaturity of the town, rather than living at the same level. By raising himself above the insult, he is able not only to diffuse its sting, but to teach his children, by example, how to deal with petty insults.