Why isn't logic taught in schools?

The Greeks, between 500–200 BCE created art and literature that inspires even today. They also invented a method of argument and inquiry that is so universally used that I figure most people don’t know it was invented. They just sort of figure it is the natural way of doing things.
It is clearly very useful and very effective at mitigating human fallibility, but it is in fact a method. Why not universally teach it in schools?