I attended public school, private school and was homeschooled during my elementary school to high school years. Having had exposure to all three environments, I feel somewhat qualified to correct statements such as this one, overheard earlier in the week: "Homeschooling is cheaper than private school."
Homeschooling is not cheaper than private school. In fact, it is far more expensive. One might argue that the benefits of homeschooling outweigh the benefits of private school and so it is a better deal, but that is irrelevant to the issue of cost. The cost of homeschooling is next best use for your time and money, i.e. your opportunity cost.
Both of my parents have college degrees in technical fields. However, in order to accommodate my wish to study at home, one of them (my mother) had to stay at home as well, giving up three years of her salary for the three years that I was homeschooled. She could have sent me to private school for all three years and given up less than one year of her salary. Or, if she valued her leisure time more than working, she could have enjoyed gardening and shopping instead of spending her day teaching me algebra, physics and trigonometry.
Representing cost as merely the dollar amount for tuition represents a fundamental fallacy in economic thinking. All costs are opportunity costs. Monetary costs make up only one part of the total cost.