Why did/do they torture people to get fake "confessions"?

On occasion: so the state may confiscate the property of the accused and disinherit his dependents.

This was the case when in 1692 Giles Corey was accused of witchcraft and refused in open court to accept a trial by his peers, instead standing mute. As the story goes Corey was then pressed in attempts to coerce an acceptance, by successively piling greater and greater weights on his chest. It's claimed that as each rock was placed on his chest, Corey kept repeating only "More weight." After a few days of this Corey succumbed; but as his estate could only be confiscated following a guilty verdict, and customs of the time only allowed a trial following a plea, his property passed to his dependents instead of the State of Massachusetts.

"Justice must be done, and it must be seen to be done."

One could argue that for the functioning of a society, the second part is more important than the first. It won't be a nice society if it regularly tortures and punishes innocent people, but it might be a workable society -- more so than any society without visible justice.

• A confession may be seen as necessary for the salvation of the sinner. That sentence brings the Inquisition to mind (Spanish or otherwise), but the boundary between secular law and religion used to be weaker than it is today. There are many legal systems where a convict who proclaims innocence will have a harder time getting parole than a convict who "comes to terms" with the crime and "repents/reforms."
  So what to do when a confession isn't happening voluntarily?
• Forensic evidence is rather new. Practical fingerprinting is a bit over a century old, practical DNA analysis goes back just a few decades. So without eyewitness accounts, getting a confession was seen as better than just circumstantial evidence.
• There were many cases/times where law enforcement would "zero in" on the suspect based on things that were not admissible in court (professional experience/instincts, or bias and prejudice). They would then have to "supply" the evidence to make their feeling stick, and a forcibly extracted confession solves their problem.

The shortest (but rather depressing) answer is that there's no enlightened logic to it at all. Its just that people under the right circumstances can do evil things to other people. We humans are creatures that are capable of logic, yes, but we're still humans.

Let's talk about one fairly well-documented case of it being used: The Bush Era "War on Terror", and its so-called Enhanced Interrogation Techniques.

Its fairly accepted academically that torture is a bit better for getting the victim to say what (they think) you want than for getting the truth out of someone. However, one thing I got from reading Jane Mayer's The Dark Side was that all indications were that both the Bush Administration people pushing for it and the people carrying it out largely honestly (but incorrectly) believed they were getting lots of good useful info out of it. Evidence to the contrary was not wanting, and in fact there are multiple cases where a false information caused real harm. However, it just seems like they didn't want to believe otherwise.

Complicating Goldsmith's efforts to push the Bush Administration's secret programs back inside the law was their reputed success. On the other side of the globe, in an undisclosed location, the CIA's clandestine efforts were more than justifying themselves in the eyes of the administration's top officials.

CIA Director Tenet for example repeatedly told officials that Kahlid Sheik Mohammed ("KSM") was providing a "gold mine" of information under torture. According to Mayer, a top CIA official asked for some of that info to share with "an allied foreign intelligence agency", and was told there actually wasn't anything solid enough to give, even in confidence. KSM later recanted a great deal of what he "confessed" under torture. As of today he is still in US custody and has still not stood trial for anything.

There was also the case of Khaled el-Masri, a car salesman from Germany, who got picked up largely due to having a fresh passport and an Arabic name, and was turned over to the US and tortured for more than a year. Internal memos show that the agents taking him in were quite certain they had an innocent man even before his plane touched down, but the higher-ups didn't want to hear it.

Almost from the start, the rendition team has a strange feeling about Masri. He wasn't acting like a terrorist. By the time their flight reached Afghanistan, the head of the rendition team sent word to the CIA station chief in Kabul that he thought something wasn't right. The Kabul station chief was incensed and sent a cable to the CTC accusing Langley of having sent him an innocent person. But the CTC officials sent back word that the head of the Al Qaeda Unit wanted Masri held and interrogated. She thought he seemed suspicious.

I have another book Becoming Evil that delves a bit more into the psychology of people who participate in genocide. That's of course different than torture, but aside from both being evil, one has to suspect the psychology involved in getting people to perpetrate them are similar. A lot of the typical elements are similar.

• A belief that you are actually the one under attack
• A culture of cruelty.
• A dehumanization of the victims.
• Blaming the victims for their own victimization ("must have done something to deserve it")
• Professional self-interest in the evil activity

I've included a couple of charts from the book below. My apologies for them being grainy photos of crude charts, but I didn't want to hide their authorship in any way.