This instant this revelation hits Laurel is at the end of the story. This "meanness" of which she speaks is something that causes human beings to seek deliberate cruelty against another. This might be due to some sadistic desire, but given the experience of the Brownies in Laurel's troop, it might be the response to cruelty done to human beings. In this, there is an infinitely regressive cycle of cruelty as part of payback and retribution, whereby individuals might feel a temporary good. However, the cycle of hatred and exclusion continues with no end in sight. It is this pattern of which Laurel speaks that represents the "mean" element in the world that she cannot stop.
If we consider the Mennonite story for a moment. Laurel's father tells her that the asking of the Mennonites to paint his porch would represent "the only time he would be able to see a white man on his knees doing something for a black man for free," this does not reflect direct sadism. Rather, it is a representation of the hurt that Laurel's father has suffered as a Black man in America. The very idea that he would take happiness in seeing "a white man on his knees" is a reference to the fact that he, himself, has been on his knees for white people. This sense of hurt is what causes him to take advantage of the Mennonite faith. It is this same "meanness" that Laurel recognizes is present in her Brownie troop in how they planned out and wished to take advantage of the white girls' troop. Even after the recognized the utter meanness in their actions, the girls are still imitating and mocking them on the bus back. No doubt the hatred of the white girls stems from the abuse they have suffered at the hands of other white people. Laurel recognizes this and her father's story as one in the same, as representative of a mean streak in human interactions, whereby the desire to exclude and intimidate is motivated by a retributive desire to do to others what has been done to them.