Why is it bad to judge an individual by the statistics of the group they belong to? I assume that drunk drivers are dangerous because many are, even though I know that some people can safely drive drunk. I assume that tigers are dangerous even though I know some are very tame — I wouldn’t hop into a tiger cage hoping for the best.

Because most of the time there is greater variation within a group than there is between groups. If you use group statistics to judge individuals you will be wrong more often than if you don't.

But beyond that, we as a society have decided that in many cases the benefits of using group based heuristics aren't worth the damage done to individuals within groups who are judged negatively.

Imagine you toss out all resumes with non-white sounding names because white people are statistically more likely to have x, y, or z characteristic. Even if there is a correlation to some characteristic that you are looking for (more likely to have a college degree, statistically higher income etc...), the damage you do to the individuals in the groups you are tossing out far outweighs any benefit you receive.

I don't quite understand what you mean by all vs average, but I think he was saying that if you have 100 random old people and 100 random young people, there will be more people in the young group that know React, for example, than in the old group.

Take that same sentence and substitute "women" for "old people" and "men" for "young people". If you used such a statistic to say "Women tend not to get React" wouldn't that be obvious sexism?