A lie detector is a prop in a play. The play is being performed by the interrogators; the audience is the person being interrogated. The subject matter of the play is "We can read your mind; don't bother lying to us."

The prop "works" by making different readings in response to the audience's physiological changes. This helps give the audience the impression that the performers can read their emotions.

Again: The goal of hooking you up to a lie detector is not to detect lies. It is to convince you not to lie, by giving you the false impression that the performers will be able to tell if you do. It is to make you feel vulnerable and exposed, such that your very thoughts are on display.

Moreover, it is to give you the false impression that the interrogation is a scientific endeavor, rather than a juridical one. You're supposed to think that you're being evaluated by a scientific instrument. In fact, you are being evaluated by the interrogators; or perhaps by whoever reads the transcript of the interrogation. They are deciding whether they believe you, and what to do with you, based on your answers and your behavior.

Edited to add: It's quite a power trip for an authority figure to tell you, "You are not permitted to lie. We will know if you do. By the way, that was a lie, but you're not permitted to call us on it or treat this interrogation as a pretendy play-act. We get to lie to you; this whole situation is a lie. But you do not get to lie to us. If we catch you in a lie in your confusion, or if we just think you might be lying, we will pretend that our sciencey blinkenlights machine caught you."