Why More Than Half Of Us Are Above Average
The apparent absurdity of the statistic depends on the assumption that being a good teacher or a good driver is a single, universal quality. If everyone is measured on the same scale, then yes, only half of us can be above average*. But things look much different if people define "good teacher" or "good driver" differently.
Take the "good driver" example. I consider myself to be an above-average driver**. And to me, being a good driver is defined by things such as "comes to a complete stop at stop signs" and "waits for a break in traffic before making a left turn." However, there is a large contingent of my fellow Arizonans who define good driving by such features as "goes as fast as they are physically capable of" and "doesn't bother with silly things like turn signals." Since those two definitions of "good driver" are not highly correlated, but people's definitions of "good driver" are highly correlated with their own driving habits, it's easy to find well over half of the population claiming to be a "good driver."
* Assume we're talking about medians here, since nearly everyone can be above the mean if the distribution is skewed enough.
** Not actually true, but let's assume it is for the sake of argument.