[fnordfnordfnord]

I am a college instructor. I think that covers "proper paedagogic/teaching education."

>You as a parent have neither the time

This part is true. Even if it weren't, I probably wouldn't pursue home-schooling my children. Neither proves the point that no person/family is up to the task.

> nor the knowledge of all the various subjects

I may be deluding myself, but I feel confident that I have mastered all of the elements of "basic high school curriculum." I expect that is true for many people. As far as any of that goes, home-schooling does not necessarily require that one person does all of the instruction, nor that the curriculum is confined to that which is within the bounds of what the parent(s) knows. In fact the parent(s) could outsource nearly all of the instruction, and merely act in a supervisory role.