I don’t think single parents can homeschool. I think it’s too scary. (There's a good discussion about that in the comments on this post.)
According to Shane Krukowski, CEO of Project Foundry, homeschooling is increasing at the rate of 30% per year. And only 38% of homeschoolers today do it for religious reasons. The bulk of homeschoolers are moms who have a college degree and a husband and live in a school district they don’t think is acceptable for their kids.
So this means that
1. The moms with a college degree and a husband are lying to themselves that the kid's school is good enough and/or that they cannot homeschool. (Don't tell me it's about the money. It's a bad excuse.)
2. The school systems should cater to helping single parents and parents without college degrees, because other parents can handle schooling on their own and should stop relying on the public to support them. (A microcosm of this issue is teaching a kid to read. My friend, Lisa Nielsen, education maven for New York City public schools, explained to me once that kids who have educated parents who read to them do not need to be taught to read — they'll just learn. The reading programs are only necessary for kids who don't have educated parents at home reading to them.)
Conclusion: Most moms lie to themselves about school, and then they send their kids there. Me, too, I guess, since I have a kid in public school. It's hard to make a good decision when public schools are the best all-day babysitting program in the world, and homeschooling demands so much time and energy from the parent doing it.