I'm afraid I have to weigh in as being adamantly against homeschooling. I worked my way through college doing special orders at an independent textbook store, way back before Amazon.com. Well, Amazon might have been around back then, but it would have been very new. Anyway, we were pretty much the only source of K-12 textbooks in that city, so we had a sideline supplying the homeshoolers. First: Only one - ONE - family ever ordered science or math books. Second: They were all crazy. They were all foaming-at-the-mouth crazy, and of course their children will be poorly socialized because they're being socialized by the crazy parents.
More than a decade later, Fox had a new reality show called 'Wife Swap', where the wife from a family of uptight squares would be swapped for two weeks with the wife from a family of crackpots. More often than not, the family of crackpots would be homeschooling their kids. Of course, the crackpots' kids were so obviously ignorant, you hoped Social Services was watching the show.
At about this same time, I had a co-worker who spent more money on his self-designed tattoos than on birth control, and thus impregnated his girlfriend. He had dropped out before high school, and was known at work as 'The Lunch Thief', because several times a day, he ate someone else's lunch on company time. He and his new wife are naturally planning to homeschool, because they're very devout Christians. Let me summarize from the details above: This guy is a moron. What chance do his children have?
I'm sure lots of people will declare that they know of homeschoolers who are smart, moral, not crackpots, etc., but the ones I've met failed at school and at life. They can't admit that their failures may be their own, so they remove the opportunity for their children to show them up. "I failed at team sports. Therefore: Team sports are stupid."
What if a pair of pretty good classical symphony musicians forced their homeschooled kids to follow in their footsteps, only to have the children grow up to be mediocre? Maybe one of the kids could have been the world's best builder of electric cars, but now the world will never know. The parents can only teach what they themselves know. Are any two people smarter than an entire school district full of professional teachers? Stop before you react with, "But, in California..." Teachers, much-maligned that they are, go to college specifically for this, get fingerprinted, get a license, and are constantly monitored. How many of these homeschoolers have had classes in education? How many even succeeded at high school?
These are just my observations, and they are subjective. But, I have met A LOT of homeschoolers.