The best example of a home schooled child is Abraham Lincoln. Parents choose to homeschool their children for a variety of reasons.
Some parents prefer for children to have lessons from a religious point of view.
Evangelists will homeschool their children because of the travel their jobs entail. Some parochial schools are too far away to attend, especially if one lives in a rural area. Sometimes private schools are too expensive. Some children do not thrive well in a public school setting. Either the child is shy or easily distracted.