The second reason, if you want to get technical, is that our home is not a school. We are educating our kids at home, rather than sending them to a school. A school is more than a place of learning. A school is “an institution where instruction is given” (Dictionary.com). Schools are designed around most effectively mass-educating children. I don’t need to mass-educate children since I only have four of them. So my home is not a school in the traditional sense. (Yes, I am aware that “school” has alternate meanings other than an institution; it can mean “to teach” or it can refer to a group of like-minded people and so on.)
The third reason is that at times, a couple of my children have attended public virtual schools. These schools are part of the publicly funded state school system and they are very adamant that we “learning coaches” know that we are NOT homeschooling! Ah, but see…we are “home educating” because the children in these programs receive their education at home–it’s simply overseen by the state virtual academy.
Interestingly enough, “homeschooling” isn’t really a word if you consult your typical dictionary. I think it should be, since “home schooling” just doesn’t flow well in my mind. “Home Educating” doesn’t necessarily have that great flow but it's a more accurate description of modern home schooling, since there are so many ways to educate your kids at home.