In the context of society at large, the responsibility for educating falls upon the parents and later on the individual in question.

It sounds like you are making an argument in favor of the whole of society being responsible for providing a benefit to the individual. I have nothing against this so long as the obligation voluntarily entered into by each member of the society. The way it is structured right now is not voluntary. You do not have the option to decline this so called "social contract". Some people may indeed have the means to leave the country where they reside, but all must land somewhere and be bound by laws which use force and coercion.

The concept that the government is responsible for the education of the children is a relatively new concept. Historically this has not been the case. Does that mean people did not get educated before government stepped in? Of course not. The current system of education was developed by the Prussians and imported into the USA. It was never designed with the intention of maximizing critical thinking, wisdom, and intelligence. It was instead designed to produce large numbers of people educated enough to operate the processes in factories, but docile enough to be packed into tight spaces for long hours to accomplish their tasks. It designed to produce good factory workers.

The best education is and always has been one on one and tailored to the individual. I am sure that there are many private sector ways to successfully teach, train, and educate our future generations without relying on The State to do so. If we rely on The State for this function, then we are abdicating our roles as shapers of the future.

"If you send your child to be educated by Rome, do not be surprised if he returns a Roman."

-Otto von Bismarck