As far as I understood it, the main limiting factor in education was teachers deliberately holding back knowledge. The main purpose of "problems", and especially of homework, was a show of social submission, designed to persuade the teachers to reveal the next secret. School one essentially one giant hazing ritual.
There's one memory that stands out as the greatest moment in my education. My school had Acorn Archimedes computers, which came with BBC BASIC, and we were allowed to program them during lunch breaks. One of the older students programmed a Space War clone. I very much wanted to write one myself, but I didn't know how to calculate rotations. The older student refused to tell me the secret, which made perfect sense according to my dominance hierarchy model of education.
I begged my math teacher for the secret, and to my surprise he actually explained how to rotate points using trigonometry. This felt like something incredibly subversive, where the teacher was giving me knowledge I hadn't earned. For this reason I still think of that teacher more favorably than any other, despite other teachers objectively doing more for me. I went on to write a superior Space War clone.
Of all the weird misunderstandings kids have about the world, this might be the weirdest I've ever heard.
I'm kinda fascinated, do you recall at what age you believed this? What was the context you grew up in (country, culture, school). Do you recall where the seed of this idea got planted?
I feel this is the most traditional and natural model of education. It's like medieval guilds, where you had literal secrets that would be revealed only after sufficient demonstration of loyalty.