Suppose a storm is coming, and landfall is projected for a location along the Gulf Coast 48 hours from now. Coastal residents in a town 125 miles away are carefully watching the weather forecasts, trying to decide how they should respond.
Anyone who might expect that 2-day forecast to be accurate to within a certain distance, say 75 miles, might think they're not going to get the storm and fail to evacuate, even in the face of local evacuation orders.
In contrast, those who have a better sense of the scales involved, whose expectations are in closer alignment with reality, may be more inclined to heed the warnings and evacuate, even though the center of the storm is not predicted to make landfall at their precise location.
It is natural for people to react to an official hurricane forecast based at least in part on their own preconceptions of how accurate these forecasts are supposed to be. People are, in effect, applying their own understanding of the advancements in modern weather science to their personal situations, all the while using cues from their social environment, the media, and local officials as guidance.
What level of precision is realistic to expect from the hurricane forecast? The answer is inextricably linked to the state of the science, which is constantly changing. Furthermore, progress is uneven: some aspects of hurricane science are improving more rapidly than others.