Aporia
Aporia - (if I'm not mistaken) this word was used in the times of Socrates to indicate that the conversation and arguments have reached a dead end. We have encountered an impasse. And the one who thought he knew something is left with a shattered worldview. Left with questions to which he no longer has answers (but previously did).
The situation is very complicated. It makes one want to cry. It feels like the ground is slipping from beneath one's feet.
Yet, does it bring us closer to some greater truth? To be on the edge of the unknown is to be closer to the truth. If our interlocutor is cunning and wise, he will question us about ordinary things. Upon understanding our thoughts about them, he will pose further intricate questions, and everything will fall apart. To us, he will appear quite rude, and it's unlikely we will hold any affection for him...