SO this guy who willingly started answering questions and got to the one he didn't want to answer should do what? Get up and say he has to go now?
I don't go around breaking the law, so I'm not predisposed to think the police are out to get *me* but suppose they are? I'm having a willing conversation with them and I realize that they suspect me of a crime and let's say it's a bad one. What do you do? Start asking for a lawyer? Simply leave?
Obviously, if you did the crime, SHUT UP from the start, don't volunteer to answer questions, don't go to the police station, find yourself a lawyer and keep his number on speed dial. IF/WHEN the police come calling, ignore any questions and tell them you need to leave right now. If they won't let you leave, go into the "Am I under arrest?" mode. If they don't say "yes" then tell them you need to leave if you are not under arrest. If they say you are under arrest, ask for your lawyer to be present for any further questions. But what do you do if you have nothing to hide?
In these days, you don't consent to searches, you don't invite officers into your home, you don't open your trunk so they can see in, you don't offer information or volunteer to be questioned unless you are simply a witness to something. Even then, be VERY careful and be totally sure you don't have something to worry about, even unrelated to the topic at hand.
But remember, you can still claim the 5th and refuse to answer the question AND they can then tell the jury that you refused to answer that question. If you started talking to them, this is your situation. If you cannot live with that, best to not talk to them in the first place.