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:
- You are more likely to answer questions, even if the answer screws you.
- You are more likely to say something in particular: loaded questions, bargains, intimidation, manipulation, doubt...
- You can't even trust your own memories.
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.