A common libertarian move, when encountering a claim about the common good, is to deny that any such thing exists. As someone said to me today, "There is no common good: only a multitude of individual goods."
Such a denial flies in the face of both common sense and the bulk of the Western philosophical tradition. Imagine the cells of your body declaring that there is no common good they share, but only an individual good to be sought by each cell on its own. We have a name for cells that "think" this way: we call them cancer cells.
It is easy to generate an example where a society of individuals each pursue what they see as their individual good at the expense of the common good. For instance, imagine a society composed of individuals who each decide that children are a bother, and get in the way of having a good time. It is obvious that on the societal level, this is suicide: this society will not survive the current generation.