As human beings, and as rational entities, we always think that we are the right ones. So, when there is an argument, we always feel that we must have the last idea in said argument, and that we must always rebut everything. The problem with this philosophy is that it never works -- because you will rebut, then they will rebut your rebuttal, etc. This just won't work all the time.
In a situation where you know this will happen, it is a far better course of action to just let it slide. This does two things: You won't have to argue as much; and, the most important reason, you will look superior. People who who do this, who question you, inflame you and insult you are just doing that to goad you into a confrontation. What better way to say 'I am better than you are' then to just walk away. To not play their namby-pamby baby games. It gives one a great sense of satisfaction, and it leaves the offending party feeling weak, helpless, empty and stupid. Just like they are.
So when a certain narrow-minded dufus taunts you by saying things like "I'm not calling anybody here a fool, except...", and you know they are just begging you to confront them on it, just chill. Just let them wallow in the solitary pathetic-ness that is their life and feel good about yourself.
Of course, I can't talk...