In an episode of a sci-fi TV series, the main character asks his opponent (or antagonist) the simple question, why. When he receives an answer he again asks why, and this repeats I believe one final time. It is a classic attempt to outwit or unsettle an opponent.
I mistakenly assumed that this segment was in the original Star Trek episode "The Changeling" though there was an attempt by Kirk to unsettle his opponent Nomad but he didn't use the above line of questioning. I'm now thinking that it may have been an episode in the original Doctor Who with Tom Baker though its just as likely to be in Star Trek.