Why are statistics useful in explaining group behavior but not reliable for explaining or predicting individual behavior?

This is the very nature of statistics. The simplest examples would be the measures of central tendency. The mean, or average, is one single number that can tell you something meaningful about any collection of "scale-level" data, regardless of how much data you have. You want to know something about the thing that is being measured, and no individual piece of data has meaning except as it affects the whole collection of data. Of course, the mean can't tell you a lot all by itself, but the following is a basic example of how the mean could be used. Someone doing educational research might want to know if a new teaching method in mathematics has had an effect on performance on a national, standardized math exam. She would compare the average (mean) performance on the standardized exam for students who took it after completing the oldmethod, with the average performance on the standardized exam for students who took it after completing the new method. There would be a need to control for many variables, and a lot more would have to be calculated than the means discussed. But if done carefully, the researcher could conclude with some degree of confidence that the new method had, or did not have, a significant affect on standardized exam performance. The performance of any individual (unless it was the researcher's daughter preparing to apply to MIT) would be of no particular interest to the researcher.