Many countries have laws that protect a suspect (or anyone else) from being forced to self-incrimination. For example USA have that codified in the fifth amendment and it's mentioned in the Miranda rights (before questioning a suspect). Perhaps it's even codified in international conventions.
What is the rationale of such law?
As with many such rights, you should look to pre-modern Europe to understand the context in which such rights were introduced.
At that time, without forensic evidence, the best chance of a conviction was a confession, and easiest way to get a confession would be to mistreat a prisoner. There was no police force so magistrates and judges would be greatly involved in the interrogation of suspects. A judge could interpret a suspect's behaviour during the interview in any way he wished. If the judge was prejudiced against the suspect, this would lead to miscarriages of justice.
The fifth amendment of the US Constitution should be seen particularly in the context of the Star Chamber, which was a court in the UK. It was used to prosecute dissenters and Puritans. Those brought before the court were compelled to swear an oath, and if their answers were unsatisfactory (i.e. not matching the King's expectation) they would be convicted of perjury. Failing to answer would be a contempt of court.
In the modern context, the question becomes, "why maintain the right to silence". In modern jurisdictions, it has become clear that confessions are unreliable, and so modern jurisprudence depends much more on forensic evidence. Removing the right to silence would put pressure on more innocent people to give a false confession.
All this is bad justice. It's unfair to the suspect, and so it is unfair to the victim.
Being arrested can be extremely stressful, especially if you are innocent since you might fear being prosecuted for something you didn't do in addition to being caught off guard.
After the arrest comes the detention, where you are isolated from the outside world and have eventually to deal with cops - and other people in detention. These conditions are even more stressful.
Take another example: something bad happened - somebody got hurt, died, there was an accident, whatever - and the police talk with you. You are stressed from what just happened and from the cops focusing on you.
Stress, exhaustion, and isolation weaken your mind very significantly. I have already gotten hallucinations just from lack of sleep. That kind of state makes you less able to fight back if people question you, and alters your perception of reality, which can be problematic in the particular context of detention of several reasons:
I'm not saying that being arrested and detained by the police is comparable to ingesting LSD of course. But being psychologically and mentally weaker than usual while dealing with people that may try to convict you and are not professional is not going to only depend on whatever actually happened. That's why you need a professional on your side for balance, and why it's a good idea to not talk until you have met with that person.
It is not a right that is there to help guilty people, it's there so that people aren't convicted for things they aren't responsible for, whatever else they are guilty of or not.
An innocent person can't benefit from talking to the police. The person concerned might accidentally say something false. Or he might say something that is true but is contradicted by a witness and the police may interpret this as lying. So an innocent person can be convicted as a result of talking to the police.
In addition, in almost every country there are many criminal offences that nobody with a lick of sense would imagine are criminal. So anything you say about anything you do may be a confession to a violation of the law no matter how innocent you think you are.
Now, you say that a criminal may use the rules to avoid conviction. This is true. On the other hand, the government has virtually unlimited resources to investigate and prosecute that person. And the government can compel people to testify. And as I noted above, there are many laws that can be used to prosecute people. So if the government can't prosecute criminals with all those advantages that would be extraordinary.
Adding to other answers, the Star Chamber gave rise to what was called the "cruel trilemma". Being forcibly questioned on oath and without warning or legal advisors, with no hint of what the questions related to or whether it was a matter involving them or someone else (maybe a family member or friend), the subject either had to incriminate themself or someone else by telling the truth, be charged with perjury if they lied or other witnesses said differently when questioned in turn, or be charged with contempt of court if they didn't speak. It was used politically of course.
The right to silence is sometimes traced to protests against this system, although hints of it existed earlier. When democratic parliamentary lawmaking came to pass, the right to not self incriminate became part of the package as a kind of reaction to the past.
In more recent centuries it was held that there were other reasons as well, mainly that it placed limits on the use of coercion and police abuse, and forced courts to look at evidence more than possibly unreliable confessions. The same area of testimony covers torture, improper searches, due process, the requirement for search warrants (why can't police "just enter" anyone's home? Similar reasons) and similar rights.
In the united states they became enshrined in the new constitution and Miranda came from the requirement to be sure that the suspect couldn't plead his constitutional rights had not been violated.
Modern rationale for such laws: police and federal agents will try to trick you into incriminating yourself, and it is ridiculously easy to do.
I was arrested on a penny-ante theft by check charge1, and such an experience is stressful for someone who's never had to deal with anything more serious than a traffic ticket in their lives2. We tend to blurt stuff out under stress that we don't think is incriminating, but sounds very different to someone who doesn't know us and is already assuming we've committed a crime. In my particular case, there was nothing I could say that would make the situation any worse (apart from something like, "wow, so this is only about the check, not the ... uh, you know what, never mind."), but as a rule you can only hurt yourself if you talk.
Shut up, keep shutting up, and let your paid legal representative do all the talking for you.
My question is what is the rationale of such law?
What would be the alternative if you would not have a right to be silent? Let's say there would be a duty to say the whole truth.
You see, there are a lot of unsolved problems with the alternative and going by the right to remain silent is at least the much more practical solution although sometimes you are actually ordered to testify and tell the whole truth. Often enough weak memories happen then.
You can assume that everyone would lie if telling the truth would mean to accuse himself. So you would still need to prove him guilty but may be forced to additionally punish him for not telling the whole truth. This may be a bit too much punishment for little gain.
With this I already included that torture is out of the question.
In addition to the other reasons given, it helps re-focus police efforts in effective crime-fighting directions.
When an innocent person is wrongfully convicted of a crime, the person who committed the crime is wrongfully enjoying his freedom and remains a potential danger to society. By removing from the police's arsenal a tool that produces a high rate of false convictions, it forces them to use tools that are less prone to error, and to a small degree improves public safety.
(I hope.)
Even if you are an innocent person, you could commit something immoral or secret even if it is not a criminal offense. For instance you could be with a lover or doing some secret business negotiation. Announcing such information may harm your private life and/or business interests, while evidence against you may be so weak so not worth disclosing such spicy things for defense.
If there was no right to remain silent, one could open a false accusation against you only to know your whereabouts at the time or other details you would like to keep secret.
In addition to my other answer, I just served jury duty this week, and the judge gave us the reason that is most important to a juror: It is a corollary of the presumption of innocence.
The judge asked one of us whether at that moment, before the trial had started, the defendant was guilty or not guilty. The correct answer was that the defendant was not guilty. This was because the state had not met its burden of proof. Until the state has done this, the defendant is not guilty.
Furthermore, the defendant has no obligation whatsoever in this regard. If the prosecution does not meet its obligation to prove the defendant guilty, the defendant can simply sit there at the defense table and do crossword puzzles or something. The defendant certainly has no obligation to help the prosecution, but he additionally has no obligation to actively defend himself. His refusal to mount a defense cannot itself be counted as proof that he is guilty.
TL;DR: The right to remain silent is the only position that is consistent the presumption of innocence.
