Homeschooling is not only superior to private schooling,
in many cases it’s actually more expensive to eschew the second income.
However, there are other considerations as well,
which are huge bonuses for the family that has a stay at home mom/teacher.
Regarding the second income....when taxes and all costs are factored in, the trade-off on the second income is more appealing in many cases than many assume. In addition, homeschooling doesn’t prevent parents from working from home - or if they have a business - bringing the children to work so they can do their school work there.
You are right, though, that there are some cases where a family would be giving up significant income.