"what homeschooling does is allow parents to teach actual history instead of the BS they make up in public schools"
Haha. Good one
What homeschooling does is allow parents to teach kids whatever they want, no training needed, no background in education needed, and certainly no objectivity needed. In fact that's the reason a lot of conservative parents homeschool their kids, so they can fill their heads with all sorts of garbage and not have anybody to explain why it's wrong.
If you homeschool your kids, you can tell them that Adam and Eve were created from a pile of dirt and a rib, and rode dinosaurs around a magical garden all day long. None of that is historically or scientifically true, but how are the kids going to know that?