Perhaps I should accept as much agreement as we have achieved and leave it at that. You have approved homeschooling when parents homeschool in the belief that they can provide a better education than can standard schools. You accept the legality of homeschooling. You see vouchers as offering an escape from wretched inner-city schools.
This discussion suffers from a lack of definition. "Education" has no simple definition which accords with normal use. In Hawaii, "homeschool" has an operational definition: legally, whatever parents do with their children after they file an application to homeschool and withdraw their children from school, subject to the condition that no court finds them (parents) guilty of educational neglect. I tutored a Korean immigrant child from third through sixth grade and continued to advise him after. His parents withdrew him from school after seventh grade and homeschooled him. This meant that they went to work and Eugene sat in on university Math classes and studied on his own. He took the GRE (Math) at 16 and got accepted into the graduate program before he turned 17.
To continue our argument...
One reason you have given for your opposition to homeschooling is that you want State-mandated indoctrination (evolution by natural selection, US History) of other people's kids, so it's not a question of whether kids receive indoctrination but of who decides what indoctrination they receive. Given ideological conformity among College of Education professors, successful indoctrination of the entire population seems to me more likely to occur through State intrusion into the education industry than through a hands-off policy.
"The terrifying thing about modern dictatorships is that they are something entirely unprecedented. Their end cannot be foreseen. In the past, every tyranny was sooner or later overthrown, or at least resisted because of 'human nature', which as a matter of course desired liberty. But we cannot be at all certain that human nature is constant. It may be just as possible to produce a breed of men who do not wish for liberty as to produce a breed of hornless cows. The Inquisition failed, but then the Inquisition had not the resources of the modern state. The radio, press censorship, standardized education and the secret police have altered everything. Mass suggestion is a science of the last twenty years, and we do not know how successful it will be." --George Orwell-- Review of Russia under Soviet Rule by N. de Basily" (Essays, George Orwell, Knopf, 2002).
"One has only to to think of the sinister possibilities of the radio, State-controlled education, and so forth, to realize that 'the truth is great and will prevail' is a prayer rather than an axiom." --George Orwell, Review of Power; A New Social Analysis by Bertrand Russell.
The market in education services
"What works?" is an empirical question which only an experiment can answer. Millions of homeschooling parents applying their unique local knowledge of their own children's interests and aptitudes will generate more information than will schools which march all students through a standard curriculum at a uniform pace. You may object that this feature of current schools is not necessary. I see two problems with this objection:
1) The State cannot subsidize education without a definition of "education", and then students, parents, teachers, and taxpayers are bound by this definition.
2) Internal bureaucratic imperatives drive standardization. The uniformity we see is not a coincidence.
The assertion that in homeschooling "you have one or at most two teachers" does not describe many homeschooling situations. Many homeschooling parents hire tutors, or send their kids to classes (Foreign Language, Art, Craft). Expanded legal room to maneuver would widen this range. Legally enforced, the opposition to homeschooling becomes a self-fulfilling prophecy (homeschooling is narrow so it must be restricted).
The government of a locality is the largest dealer in interpersonal violence in that locality. People do not become more intelligent, better-informed, more altruistic, or more capable (except to the extent that they have access to violence) when they enter the State's employment rolls. Wherever markets fail, governments fail also, except in the few cases where monopolistic control of violence is beneficial (war, crime reduction).
Pareto equilibrium versus Kaldor-Hicks equilibrium? How did this enter the discussion? We were discussing the market as an information-generating mechanism. Absent compulsory attendance laws, homeschooling parents are the free marketplace of ideas.
I do not see the point of using percent of GDP as a measure of education costs. Of course the US could afford to spend more on the NEA/AFT/AFSCME cartel's schools. We could pour billions down other ratholes as well. Bill Gates undoubtedly spends a smaller fraction of his income on food than I do. Is he therefore malnourished? Basic literacy and numeracy contribute to economic growth. Above this rather low level of education, State support of school is just as likely to be a drag on the economy. Legal treatment of property and capital, transparency (anti-corruption), and the tax system matter more than percent of GDP devoted to education.
You write: "Most of us think that it isn't a particularly bad thing that kids have to get an education...". Under current law, children "have" to attend school. If school is a means to the end of education, since homeschoolers typically outperform conventionally schooled children, both on standardized tests of academic achievement and on measures of social adjustment, why would you not prefer homeschooling?
Compulsory, unpaid labor is slavery. Compulsion and compensation are matters of degree. Compulsory attendance laws require compulsion, obviously. Children, especially very small children, will work their hearts out for the love and approval of parents. Schools cannot match this compensation, and it's very dangerous for them to try. Later, self-directed study is self-motivated and internally rewarded. Compulsion kills motivation, as Einstein observed.
School as an impediment to education
The success of some schools (e.g., magnet schools with voluntary enrollment) does not rebut the generalization that compulsory attendance and the uniform pace and the standard curriculum stifle the development of many kids. The complexity of some jobs in modern society (e.g., engineering, surgery) indicates to me that society would benefit if some kids started specialized training earlier. Did you read that Marvin Minsky comment on school which I linked earlier? Here is another advantage of homeschooling.
The way to teach tolerance of diversity is to tolerate diversity.
Teachers versus parents as taxpayers' agents
Parents are more reliable agents. Raw numbers of abuse cases are not informative. By analogy, more humans die at the hands of other humans than are killed by sharks, but I'd rather walk the length of Kalakaua boulevard at midnight 100 times than swim the mouth of Pearl Harbor at midnight once.
Teacher certification is a joke. It does not screen child molesters and does not certify subject-area competence.
The system generated these corrupt standards and the more resources taxpayers pour into it, the greater the payoff to insiders to corrupt the standards. The most reliable education standard is the parent standard: "do I want my child in that school?"
Have you read any doctoral theses in Education? I have. They are...rhymes with "theses". Whole Language did not fall to criticism from other experts "in the field", it fell to criticism from professors of Psychology and Linguistics with tenured positions in prestigious universities. Pure "argument from authority". The argument was correct, but the authority was all that mattered to the idiots in Colleges of Education.
Every law on the books is a threat by the State to kidnap (arrest), to assault (subdue), and to forcibly inoculate with HIV (imprison) someone, under specified circumstances. Seems to me, it's the advocates of violence who bear the burden of proof.
This post updated with the observation on the difference between "school" and "education".