When the police tell you anything you say “can and will be used against you in a court of law,” they mean it. You have no way of knowing what, exactly, you will be eventually charged with, and just about everything you tell a police officer could help a prosecutor in some fashion.
Many cases are simply the word of one person against another. The police are prevented from testifying about what a complaining witness told them by the Confrontation Clause of the Constitution and by the rules of evidence, but the police are allowed to testify about what a defendant says. If you tell the police anything that can help the prosecution, you’ve just given them more witnesses. Most laypeople are not very good at testifying in court. They get nervous, they’re unsure of themselves, and they wander off topic. Police officers, on the other hand, make very good witnesses. As part of their training, they take classes on how to be better witnesses, and they’ve testified in court many times before.
Take, for example, the crime of making criminal threats (covered by Utah Code §76-5-107, but illegal in nearly every state.) Let’s say that Mr. Jones is accused of threatening to punch Ms. Miller. As is often the case for this particular crime, the only corroborating evidence is the phone record, which only proves that a telephone call occurred. Fundamentally, the case boils down to Ms. Miller’s word against Mr. Jones’s. The judge or jury must believe Ms. Miller beyond a reasonable doubt, but she might have a hard time remembering the exact words that made up the criminal threat. The police officer, however, took copious notes. Because Mr. Jones talked to them, the police have pages of notes to remind themselves of what exactly he admitted, and they are able to tell the court in detail. So even though Mr. Jones denied making any threats, the police are able to testify that Mr. Jones admitted they had an argument over the phone. The confident, polished police officer will seem very credible to fact-finder, and Mr. Jones now has twice as many witnesses against him.
Also, police officers, like everyone else, are prone to error. Police officers sometimes mis-hear or mis-remember what they are told during interrogation. Through no malice on the part of the officer, they can testify that you said something you haven’t. If you never talk to the police in the first place, there will be no question about what you did and did not say during the interrogation.