How old must a child be until they are wholly fit to make their own decisions? How do you define public policy around this, written to incorporate the whole of the public and not just the outliers? It is absolutely impossible to try to give special exceptions on such a large scale. This leads states to define a minimum age at which a child can give full consent and be legally bound to contracts.
States don't just define a minimum age of consent. They consent on behalf of children. In that sense, we can compel them to go to school "without their consent," so to speak, because the state is the only institution that can really legitimately claim to consent on their behalf.
The state has stronger claims over children in some cases than their parents do.
For what it is worth, working on the farm as a youngster brings some of my fondest memories of childhood. I find it rather sad that people outside of the agriculture communities do not have similar opportunities until they grow older.