Only a fool tries Perp Sweating a brainy killer. He knows all the tricks of psychology, and will turn the tables.
The creeper starts out with a few seemingly-innocent questions about the interrogator's life or even appearance — "Why did you go into law enforcement instead of medicine like you wanted?" or "Why aren't you married?" Then, the supposed loon asks more armor piercing questions, which turn into comments, which turn into deconstructions, which turn into declarations about how the interrogator has failed in different ways. Pretty soon, the loon is doing all the interrogating and all the answering, with the poor "interrogator" doing nothing but nodding their assent and crying.
In the climax, the prisoner's probing becomes a full-blown breaking lecture. This method of 'interrogating the interrogator' is a subtype known as a Hannibal Lecture. The theme of the lecture is always the same: their captor is a sad, pathetic failure who is only holding the prisoner captive to give themselves delusions of adequacy. Frequently, the captor must admit they aren't so different morally.
A Deconstruction or subversion may involve the killer trying this on the interrogator, only to find that the interrogator is Too Dumb to Fool and doesn't understand why he's supposed to feel bad about whatever the killer said. Either that, or the interrogator simply doesn't care about the killer's opinion.
Incidentally, this trope is why professional interrogators for police and other investigative agencies are trained never to answer questions. Ever. The main protagonist of The Closer is one of the few interrogators on TV who is faithful to this basic precept. Movie Nazis tend to respond with "Ve are askink ze qvestions here!"
Named for Dr. Hannibal Lecter of the 1988 novel The Silence of the Lambs, who set the standard for this trope when he was immortalized onscreen by Anthony Hopkins in the 1991 film adaptation. You can't spell "Lecture" without L-E-C-T-E-R U!
Sub-Trope of Break Them by Talking, where you'll find examples about someone who's not being interrogated doing it.
See also: To the Pain, Talking Your Way Out, Just Between You and Me, Evil Gloating, Shut Up, Hannibal!, "The Reason You Suck" Speech, Critical Psychoanalysis Failure, and Mirror Character. Compare And Then What? If the declarations come from simple clues, this is a form of Sherlock Scan. Compare Kirk Summation, which is where a hero boils down a villain's Evil Plan or Motive Rant. Contrast Defiant Captive. Works employing this trope usually imply a fairly strong stance on The Power of Language.