I think teaching is actually a bit of a rarer skill than that. I agree it isn't necessarily learned simply by having done a teaching course, but whilst it might be something most people can do on some level, to be able to do it well is, as with a lot of things, a different level.
Teaching adults in the workplace is different to teaching children. Adults have a vested interest in learning how to do their job. Despite the plethora of parents on here whose children are these amazing independent learners who just love to research, etc, a lot of kids aren't like that.
Parents with those sorts of children will often say, 'oh, but all kids are like that if you do this, this and this', but they really aren't.
As a teacher, whether at home or at school, you have to be able to get kids to do things they don't want to do. Because not all kids will enjoy every aspect of learning things they need to learn. Given the battles some parents here have just with getting their children to clean their teeth, etc, I can imagine having to play that out with academic learning as well takes a lot of thought, research, and, yes, skill. At least teachers can leave it behind at the end of the day.
Any lesson a child doesn't want to learn is a hard one. You have to be patient. You have to not put them off the subject. You have, with some children (and I was one of these, so I know what I am talking about) to get past a natural indolence towards anything they don't find easy (and in my case, that was most things).
In addition, if you have more than one child and one is more the independent study type and another needs chivvying all the way, that's a dynamic to manage.
Teaching is a skill that we really don't think enough of, until our kids aren't being taught well. I think it's a good thing if OP genuinely recognises she might not have it. Many teachers in schools don't have it. You can be the brightest star there is at your subject academically, but still be useless at teaching it.
And unfortunately, whereas music teachers can and do lose students who have no real aptitude or interest, you can't simply drop maths or English if the child isn't that into it.