[the]

Not a huge sample, but most of the ones I've known have done it because the kid has some problem dealing with other kids and/or otherwise coping at school.

So rather than address the underlying issues (the kid is going to have to deal with the cold cruel world without being tied to mommy's apron strings sooner or later), the parents eliminate the immediate problem (i.e., the other kids/school).

I suppose if one lived in a remote area or one which otherwise had no decent other alternative. But hard to see why one would do that in an area that had regular (either public or private) schools available to them.

The kids in your example, how old are they now? IMO, they could be fine now, most kids would like to stay home with mommy. But there's just a lot of socializing and other lessons, not all of which are fun but are valuable, that can't be duplicated by mommy.