I want to discuss three modes of child education: (1) State-directed learning, (2) Parent-directed learning, and (3) Child-directed learning. The first is clearly unethical and should be rejected.
The Unschooling philosophy is that children learn best when they direct their own learning. "Go to school / learn this now... or I'll spank you!" and "Go to school / learn this now... or you don't get any tea!" are examples of parent-directed education. Saying "Go to school / learn this now... or I'll be very disappointed" or "Go to school / learn this now... is my advice" would indicate child-directed education. There are continuum issues about what constitutes true child-directed education; the age of the child is a factor. But the distinction between child-directed and parent-directed learning is an important one.
An analogy can be drawn between parent-directed vs. child-directed learning, and statism vs. anarchism.
The parent who directs his own child's learning is assuming that a child cannot or will not learn the things they ought to learn. The mindset is one of 'taking control', setting goals, making measurements and determining what should be learned, like a statist, rather than a mindset of letting things play out naturally, trusting in liberty and markets, like an anarchist.
Unschooling advocates disagree with the idea that a teacher (or parent) should have 'core objectives' that they direct their children to learn. Children learn things because they want to learn them. Who says that anything needs to taught as a 'core skill'? Take reading and writing. Obviously a person will struggle in life (to say the least) without these skills. But because they are so important children recognise for themselves that these are things they need to learn, and that's why they learn them. A child does not need to be given motivation; the motivation comes from within.
Is it important for a person to know Pythagoras' Theorem? Maybe; it depends on what that person wants to do. I think we can leave it up to the child, whether they want to learn it. If they want to be an engineer, they will surely learn it themselves without being directed. If they want to be an actor, maybe it would be better if they spent more time in drama classes rather than maths classes.
There is even a manifestation of the economic calculation problem, which plagues all state monopolies. A state monopoly (such as state-run security, roads, or healthcare) cannot know whether it is using resources efficiently for satisfying consumer desires, because it has no feedback mechanism. Free market firms are able to calculate profits and losses because of the existence of market prices, which provide instant feedback on supply and demand conditions. Free market firms can then be sure that they are using resources efficiently, while state monopolies can only guess at how best to use resources.
How can a parent, who is directing his child’s education, know what is best for her child, the best way her child learns, and the best way to facilitate this learning? Without letting the child decide, the parent cannot know whether any given skill or knowledge is desired or useful, or how much of the child's "learning time" and resources should be spent on each subject. They can only really guess at these things. But by letting a child direct their own learning, the child will demonstrate his desires through his actions, and try to attain his ends as efficiently as possible. With parent-directed education, the lack of a feedback mechanism makes economic calculation with respect to education impossible.
Children learn best when they direct their own learning. The proper role of the parent is to facilitate and advise, not to direct.