11th and 12th classes also qualify as school (or high school).
In school, you teach general subjects like physics, chemistry, accountancy etc., which in itself, will not be sufficient for a student to work as a chemist or accountant etc.
In college, students are taught a certain specific skill to enable them to obtain a job in a certain profession. Teaching aspects are much more challenging and teaching at college level requires a different skill set compared to school (high school or post secondary school as you put it).
In any case, from what I have read in this forum, there are plenty of school teachers who apply under 4131 because of this confusion. Unfortunately, immigration officials do not accept those applications.