Those who control the means of production, which is to say, the capital, are the owners. Under socialism, the state controls the means of production for everything, from farming, to mining, to schooling, to entertainment, to religion, even procreation itself, as we see in communist China. The state is omnipotent, the individual of little account, the family, even less. I n mining or farming, capital consists of owning lands, for the wealth produced here is from the land. Since education is not a good, but a service, the means of production consist primarily of owning the costs of service delivery.
Ownership is control, and viceversa.
It is because the government owns the means of producing education that it can compel attendance and control curricula. Everything about the education monopoly we dread is a manifestation of the government's funding monopoly. So if it's wrong fundamentally, distributing it a little wider won't make it right. Which brings us to vouchers. I do not oppose vouchers because they will burden private schools with onerous regulations, or because they will lead to the secularization of religious schools, the homogenization of private and alternative schools, weakened families, the expansion of the unions, increased costs, and yes, decreased test scores.