Just to be clear since I have made comments about homeschooling and being largely against it; I can certainly appreciate that there are qualified people who homeschool and do make sure that their children are socializing and are being taught from a comprehensive cirriculum which is age appropriate and will prepare children for higher education.
My reservations against it are based on the ones that aren't qualified and don't prepare children for independent life and higher education and I know there are far too many of those sorts of home schools.
A kid may learn more about cultures of the world by traveling but will notice huge holes in their education and ability because they don't know how to use a credit card, a bank account, set up a retirement account for when Jesus hasn't come back yet, set up accounts to help their children with a college fund so they don't end up as burnt out baloonies or canners or whatever.
Schools don't teach how to use a credit card (or how NOT to!), about bank accounts, or how retirement funds work. They SHOULD. But they don't.
I came to homeschooling rather unwillingly after being convinced that I would NOT allow the sins of my miseducation to be visited upon my children. And in the beginning, I largely agreed with you. BUT...and here's the huge BUT...as poorly as homeschooling serves a small minority of students, public school's track record is far worse on every account and in every study, including those done by people aiming to discredit homeschooling.
A parent without a high school diploma who homeschools will have chilldren who, on average, out perform not only public-schooled children with parents with low formal education but will out perform that AVERAGE student. Homeschooling is the ONLY form of education in which the standardized test results show NO statstically significant difference based upon income, race, or parental education. These results are, frankly, staggering, since so many people have tried--and failed--to escape from socioeconomic determinism by moving to a new town with better schools, or providing more funding to schools, or adding more programs to schools, etc., etc. The inequities of race, wealth, and parental education continue to haunt public school students no matter WHAT school district they move to or HOW well their school is funded. And yet all such differences simply disappear when parents homeschool.
Depending upon the study, the average homeschooler scores in the 60th to 85th %ile on standardized tests. That should give you an idea of how miseducated *some* group of students is.
Does that mean that homeschooling should be for everyone? NO. There is a reason why homeschooling has those results--by and large, parents who homeschool care about their kids' educations. With the advantages of one-on-one tutoring and the correlation between parents' self-efficacy in their children's education and actual educational attainment, the positive results are much less surprising. Any parent who doesn't care about their child's education--intensely and personally--should not homeschool. It's also true that homeschool failures don't stay in homeschooling, while public school failures stay in public school all the time. Some parents just can't do it, will fail, and will send their kids back to "regular" school, where they become public school failure.
And yet... Several years ago, I would have stated that those who are largely uneducated themselves shouldn't homeschool. But the statistics STILL show firmly that their kids, however imperfect the education they receive, are better off with uneducated parents homeschooling them, if they can make it work, than going to a public school with the same background. Hard to deal with, but true.
In many ways, homeschooling statistics don't tell us how good homeschooling is but how bad institutional schooling is.
I still support madatory standardized testing for checking for a minimal level of educational attainment, to find and protect that small minority whose parents aren't educating them appropriately. The question is, will the students do any better in a public school? Unfortunately, the answer is, "maybe."