"But the 'teacher' need not be employed as a teacher. The teacher could just be one of your parents."
Yes Nigel they could (in fact my Mother was a teacher) but who teaches the parent.
I somehow expected more from you Nigel.

Nice try. I didn't expect more from you.
If anything can only be taught by a teacher, or (as you say) by someone who was taught by a teacher, then ultimately no-one will ever have been taught anything, as there must be someone back at the beginning who learnt for themselves. If that is the case, there can still be those who learn for themselves.
Teachers, as a profession, help to standardise what is being learnt, with all the possibilities that includes for indoctrination, or continuance of error.

Some teachers are excellent, and I have been fortunate in being taught by some. But they are not all of the same quality.