Why might the range not be the best estimate of variability?

It may be because the range isn't actually considered an average, it's shown using a box and whiskers diagram, Mode is the most common number. Mean is all the numbers added up and divided by the amount of values there are in the adding up process. so overall the range is less useful to show variability as it only shows the lowest and highest number in the data, and not the different individual numbers variety amongst the results