One of the first things a politician will due when he doesn’t have a counterpoint is resort to ridicule. It’s a sure sign that he doesn’t know how to argue against your point, otherwise why wouldn’t he make a counter point.
It’s the same thing here. When somebody blows up at me and calls me every name in the book, I know I said something they couldn’t counterpoint.
And I make it a big point before I turn to leave the encounter, usually in the form of a question they cannot answer because it demands self retrospect and thought.
But the will remember the encounter every time they see me again. Therein lies hope that thought and not reactive emotions will somehow get through. Whether it does or not, they know not to start the silliness again.