The problem is that no matter what the other believes, if it runs counter to your logic then they can't be right in believing as they do. The counter to your reasoning is if their reasoning is based on existential experience. They will then tell you that they do not believe, they "know". You cannot possibly have a offence argument to that. Since you have not experienced what they have experienced then it will seem illogical, irrational and unreasonable to you. If they say that they "saw something" then your logical reaction is to blame their brain chemistry, that they were hallucinating. Here's the thing - hallucinations are real to the person experiencing them, just as a child who cries after having a nightmare cannot tell the difference between nightmare and reality. You also probably experienced the same thing - where upon waking you can't tell the difference between where reality starts and the dream ends. Both perceptions exist within the mind as real. If the mind can be fooled by illusion why can't it be fooled by reality? With greater awareness comes seeing what others don't see. For example, the old saying "you can't con a con".
We all insist upon Logic and Reason as being Acme and then do stupid things - like getting drunk, doing drugs, falling in love, or getting angry. Why? A driver cuts you off, you get angry and logic flies out the window. We are emotional animals. To say that we are wholly rational is disingenuous.