Neither Hoppe nor I say that education must be provided entirely within the confines of the nuclear family. Hoppe allows for education "produced and distributed in cooperative arrangements within the framework of the market economy."
I talked about arrangements that are outside the framework of the market economy.
It's a false dichotomy to say that the only two choices are public schools (or private schools as little more than public school substitutes), and homeschooling, defined as where all education takes place within the nuclear family.
The other point that Hoppe is making, I think, is that education is just none of the business of the state. Yes, folks can make arrangements for education that make extensive use of resources outside the family. But Hoppe's point (and mine) is that these should be entirely voluntary, not forced by the state, and entirely within the control of the family.
Although education outside the home is ancient, I'm pretty sure that compulsory, universal education is a relatively modern invention.
sitetest
(1) Could you expand on what you mean by education if it needn't be the exclusive province of either individual families, on the one hand, or public (and private) schools, on the other?
(2) I can't agree with you that education is just none of the business of the state, if by the 'state' you mean the system of laws and institutions that make up a nation such as the United States. It would be the most extreme folly for the leaders of the U.S. to take no interest in the education of U.S. citizens, and to give up trying to insure that a certain level of educational achievement is reached by all citizens (we both know that there's not as much success in the endeavor as there ought to be, but I'm talking about the principle of the thing right now). We no longer live in small groups of a few tens or hundreds of family members and friends who share a world view and skill sets.
(3) You write: "As to who can successfully homeschool, my own experience suggests that nearly every mother with the equivalent of a mediocre high school education is capable of educating her children through at least eighth grade." Maybe. But what happens after eighth grade? Who takes over?