In my opinion, no child, except one with very poor health, should be home schooled.
Part of education is socialising children and teaching them that different groups of people do things differently and hold different views. They are n ot going to learn these things if they stay at home, either being taught by their parents, or by a teacher employed by the parents. After all, who would chose a teacher that has radically different view to those they hold themselves?
No parent, whether a teacher or not, nor any one teacher can be expected to have sufficient knowledge of every subject that schools teach, so home schooled children tend to be good at the subjects whoever taught them enjoyed and was good at, and ignorant of anything else.
This is not a good preperation for adult life. If a home schooled child is to have the qualifications necessary to get into a university, training college or the forces, he or she is going to need to take exams around the age of 17 or 18, and most home schooled children will not know enough to do so.