In this paper, I argue that the more objectively desirable children's formal education is, the stronger are the moral reasons to conceptualise the school normatively as a public social institution. Social institutions are goods-producing teleological entities for which the good created provides a central framework for the normative evaluation of the institution. The intrinsic value of desirable human goods morally obliges both their collective availability and collective production that, on a large scale, is possible only via public social institutions. In contrast, private social institutions are disposed to produce goods whether instrumentally or exclusively, and thus, within private institutions, the production and distribution of the desirable goods is easily compromised for private purposes, such as for monetary profit, ideological gain or the internal coherence of a social group. Privatisation of desirable goods thus endangers their collective availability. Moreover, private social institutions are required to bring forth the aggregated interests of their members that might only have an arbitrary connection to desirable goods, whereas public institutions are morally and politically responsible to the general public to guarantee the collective availability of the goods that they produce. Therefore, if children's formal education is considered a desirable good, it is also a collective good that ought primally be publicly produced.