"New Year's Eve meeting" is not an official name.

The New Year's Eve meeting is a meeting that supposedly grownups attend on New Year's Eve every year, where they tell other grownups of the rotten things that they did to their kids and dream up new ideas for mean things to do to them.

Buster told Arthur that he heard of this meeting from his cousin after Arthur told him what Binky told him about there supposedly being a New Year's wrestling match. In Buster's imagined meeting, a father says that he told his kids that spinach is good for them, even though they all know that they just love the funny faces they make when they eat it. A mother proposes the idea of no increases in allowance the next year, to rousing applause.

That evening, Arthur wished for his parents to "have a nice meeting" before they left for a New Year's Eve party, earning him an odd look.