I think Billdo has a great deal of the reason. Self justification is a powerful motivator to speak. And people realise that persuading the police of innocence (which they think might be a good idea) requires looking open and cooperative - as soon as you put the shutters up, you know that you have lost that advantage.
Also, often what police get from an interview is not a confession but a provable lie of the “I did not have sexual relations with that woman” type when they know they have DNA there. That can be incriminating too, even if the person was hoping it would have exactly the opposite effect.
Generally, people aren’t wired for awkward silences. They know that if they are accused of something in ordinary social interactions, they would be expected to respond. The police use those ordinary social expectations well.
Some police I know love silences. They ask a question, get an answer (a denial) then just sit there and stare disbelievingly and say nothing. Eventually, suspect fills in the silence, to add further detail or to explain or expand, whatever. He who breaks first loses in that game, because once you have the suspect engaging in conversation, the usual social norms kick in, and the suspect becomes as garrulous as he would in any ordinary conversation, and the police can then lead them on and trap them, or use whatever other trick they have up their sleeve. As long as you get them talking.
And some start wanting to talk so they can tell a lie, and as they go, they have to adjust and modify and fall back until it is all a hopeless disaster. “I wasn’t there. Alright, I was there, but I didn’t see her. Alright, I did see her, but I didn’t have sex with her. Alright, I did have sex with her but I didn’t rape her. Alright, she did say no, but I didn’t believe her.” Some people seem to think that for each version they give, they are entitled to a restart, so that only the final version gets used against them, and not all the earlier false starts which put the lie to the whole account.
People have an instinctive sense of what part of an accusation being made has the ring of truth so that a blanket denial will be implausible, and try to fit an excuse around it, not realising that their answer comes across as implausible and contrived, and they have admitted significant aspects of the complainant’s story.
So I guess the answer is there are all sorts of reasons why people talk to police when they don’t have to. But saying I don’t want to speak is not as easy as you might think when it is all going down. Experienced crims have learned to do it, but first-timers (and most murderers are first-timers) are still caught up in the ordinary social expectations of conversation, where questions invite answers, and accusatory questions require a response.
In my jurisdiction, the police did not video tape conversations until the mid 1980s. Prior to that, they were recorded in writing. Experienced defence lawyers here assumed as an absolute article of faith than no-one ever really confessed (why on earth would you?), and the written documents were either fabrications made up like movie scripts out of whole cloth, or where there were signatures, the suspect was coerced. The whole criminal justice system, they thought, was being conducted on the basis of a giant fraud. Every single trial where there was a confession resulted in a huge fight about the genuineness of the confession.
They were very much in favour of video-tapings, because they thought confessions would end.
Instead, they were utterly astonished when they saw large numbers of videos of obviously uncoerced people confessing away happily. This was a shock to their world view.
Nowadays, confessions are rarely challenged as they once were (again, speaking of my jurisdiction). That does not mean that all is hunky dory or there aren’t dodgy things done to induce them, etc. Just that a cultural assumption that no-one actually confesses has faded into the past.
