According to Esolen and his reading of Pope Leo XIII's writings, a family is a true society and must be obedient to legitimate authority. The leader of a family is the father, whose authority comes from God. (This, of course, does not mean that the father is better than the mother.) The father himself must be obedient to God and faithful in his duties. In particular, husbands should "live considerately with your wives" (1 Peter 3:7), and fathers must work together to establish good schools for their children.
More generally, parents must (and have the right to) teach their children about what is true and right, including the truth about God and His creation. A solid education starts with sound philosophy (such as that of St. Thomas Aquinas), for true philosophy leads one to God.
In a family, a child has a history, a place in the story of creation, and a relationship with God and His people. In a family, a child learns to live with others and to live for others.
On the other hand, what will a government without God teach? It will teach that marriage is an agreement defined and controlled by the state; that divorce should be simple and marriages are temporary; and that the state should teach the children because transient parents cannot. In this way, the state will remove fathers from families and corrupt their children, who will learn nothing except the "most abject theories of Materialism."