You can't not think in terms of stories, that is simply how our minds work. All you can do is to try to keep that (in the form of "intuition") from preventing the adequate weighing of statistics, probabilities, and explicit evidence that can't easily be fit into narratives.
Added: Even when thinking with images or kinesthetically, a person can only use the images or feelings as isolated "facts" or as part of a consistent sequence which has all the same problems as verbal stories.
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: