You can have some fun with people whose anticipations get out of sync with what they believe they believe.
I was once at a dinner party, trying to explain to a man what I did for a living, when he said: "I don't believe Artificial Intelligence is possible because only God can make a soul."
At this point I must have been divinely inspired, because I instantly responded: "You mean if I can make an Artificial Intelligence, it proves your religion is false?"
He said, "What?"
I said, "Well, if your religion predicts that I can't possibly make an Artificial Intelligence, then, if I make an Artificial Intelligence, it means your religion is false. Either your religion allows that it might be possible for me to build an AI; or, if I build an AI, that disproves your religion."
There was a pause, as the one realized he had just made his hypothesis vulnerable to falsification, and then he said, "Well, I didn't mean that you couldn't make an intelligence, just that it couldn't be emotional in the same way we are."
I said, "So if I make an Artificial Intelligence that, without being deliberately preprogrammed with any sort of script, starts talking about an emotional life that sounds like ours, that means your religion is wrong."
He said, "Well, um, I guess we may have to agree to disagree on this."
I said: "No, we can't, actually. There's a theorem of rationality called Aumann's Agreement Theorem which shows that no two rationalists can agree to disagree. If two people disagree with each other, at least one of them must be doing something wrong."
We went back and forth on this briefly. Finally, he said, "Well, I guess I was really trying to say that I don't think you can make something eternal."
I said, "Well, I don't think so either! I'm glad we were able to reach agreement on this, as Aumann's Agreement Theorem requires." I stretched out my hand, and he shook it, and then he wandered away.
A woman who had stood nearby, listening to the conversation, said to me gravely, "That was beautiful."
"Thank you very much," I said.
Part of the sequence Mysterious Answers to Mysterious Questions
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I'm not sure. The kind of irrational beliefs you're likely to talk about with others are some kind of misconception or cached belief, rather than an out-and-out delusion like "people are following me everywhere", which probably stems from a chemical imbalance and can't really be talked away.
You could try reading up on CBT, but the literature is about doing therapy, which is a pretty different animal from normal conversations. Active listening might be a more useful skill to start with. People are less defensive if they feel you're really trying to understand their point of view.