>> What is it about teaching that makes people with no training think they can do better than trained professionals?

Teaching one or two students whose home situation supports you 100% is a much much less daunting proposition than trying to teach a class of 30 kids (or several such classes).

The idea that teaching things to your own children (which all humans have done forever) requires specialized training and credentials seems silly. But again, that's a very different job than being a school teacher, I think.