Sure, by using the framework and infrastructure provided by the State, someone like Myrkul can easily tell their kids "go to the library and borrow a book on the subject". However, without a government to absorb the costs, free libraries almost certainly wouldn't exist. And if Myrkul disagrees, perhaps he can demonstrate his Capitalist prowess and explain how free public libraries would be possible under a government-free system like An-Cap?
I'm all for having professionals teach students instead of unskilled parents (I really dislike homeschooling), but library? Are you serious? When was the last time you've been to one? It has been years for me, and I was in school not too long ago. We used PDF articles and study materials on our computers and tablets, and PowerPoint presentations as study guides, and used the internet (even Wikipedia) to do our reading and research. All out-of-copyright classics required for reading in English lit classes are freely available as well.
As for the rest, I'm not saying that's how it will happen, but in an AnCap society, without a centralized government social system dividing us into counties, precincts, and countries, we could have people form social groups themselves. For example, a poor immigrant community might form a tribe of sorts (Neil Stephenson called them phyles), which will want to compete against other groups in the market financially
and socially. To do that, they might put social pressure on each other to do well with raising kids, and even have their own dedicated educator that is willing to take poor kids in for free. Remember, they are not competing based on the teacher making a profit, they are competing as a corporation, trying to get their kids to either run more successful businesses than their neighbors, or get into more prestigious positions elsewhere.
