Weaning a child, drying off a cow and giving up a habit were all traditionally scheduled for the waning moon, when things are supposed to decrease.

It is the same waxing-adds, waning-removes logic as every other item on the list, applied to the hardest thing on it. Appalachian and Central European almanacs both carry the rule. There is no mechanism, but there is a real practical benefit to picking a date in advance and telling other people about it.