Tyler Cowen argues in a TED talk (~15 min) that stories pervade our mental lives. He thinks they are a major source of cognitive biases and, on the margin, we should be more suspicious of them - especially simple stories. Here's an interesting quote about the meta-level:
What story do you take away from Tyler Cowen? ...Another possibility is you might tell a story of rebirth. You might say, "I used to think too much in terms of stories, but then I heard Tyler Cowen, and now I think less in terms of stories". ...You could also tell a story of deep tragedy. "This guy Tyler Cowen came and he told us not to think in terms of stories, but all he could do was tell us stories about how other people think too much in terms of stories."
There's more than just the one non-failure mode to this kind of thing. My method involves taking the time to consider the information gathered up to the point where I decided to stop listening to the person, as if I hadn't stopped listening to them at all. Information that I would've gotten from them after that point isn't affected by my opinion of them, since I haven't heard it (where it would be, if I were distracted by thinking 'this person's an idiot' as I listened to them), and I give as fair of a trial as I'm able to to the rest.
It may also be noteworthy that I didn't judge him for an argument he was making, and I make something of a point of not doing so unless the logic being used is painfully bad. (Tangential realization: That's why activists who aren't willing to have any 101-level discussions with newbies get a (mild) negative reaction from me; discarding a whole avenues of discourse like that cuts off a valuable, if noisy, source of information.)