The answer is surprisingly simple, although the advice is rarely followed. Unless you absolutely have to answer a question, you should never talk to the police. Anything that you say in response to police questioning is likely to make your situation much worse.
If the police are questioning you, they suspect you have committed a crime and are looking for further evidence to allow for your detention or arrest. If they have already detained you, they already believe they have a case against you, and now they would like for you to help them out by talking. Confessions are a prosecutors best friend.
The police are not going to believe anything that you say. Talking to them will not prevent you from getting arrested. The police already have evidence suggesting that you committed the crime, that’s why they are talking to you in the first place.
Many people think that because they are innocent, or highly educated, or any whatever other silly reason, they think they can talk to the police and convince the police not to arrest them. Many of these people have gone on to become my clients. If they had only remembered that you should never talk to the police, perhaps they never would have become clients in the first place.