Oh, boy, we can get ethymological about this and get nowhere.
I have heard the lines that "education" stems from the latin "ex ducere", "leading out" — which basically means developing, unrolling. But it needs to have a leader (a Duce) whom to follow.
I have also heard people argue that "education" likely stems from "ductilis", from "making a person more ductile", more likely to follow their assigned roles in society.
I have heard people insisting we should strongly favor "instruction" over "education", because it has much less an ideological bend. Instruction is the communication of knowledge, of facts and skills.
Mind you, in Spanish we don't use "schooling", and I don't know exactly how it should be translated. But anyway — Education includes human, social, behavioral aspects over instruction. And I feel that schooling strongly emphasizes on said aspects. Schooling also goes about the importance of the society going all together and coordinated — There are standardized school subjects to be taught. A person cannot say he has enough education to enter productive life if they never learnt the rudiments of algebra (for abstract thought), physics and chemistry (for a basic understanding of how the world around us works), language and literature (to be able to express oneself and to understand others), and a very large etcetera that will eventually include all of the subjects me or you used to hate in school.