Here is quote from Samuel Miller in his excellent little book, “Infant Baptism.”
The truth is, one great purpose for which the church was instituted, is to watch over and train up children in the knowledge and fear of God, and thus to , “prepare a seed to serve him, who should be accounted to the Lord for a generation.” And I will venture to say, that that system of religion which does not embrace children in its ecclesiastical provisions and in its covenant engagements, is most materially defective. Infants may not receive any apparent benefit from baptism, at the moment in which the ordinance is administered…still the benefits of this ordinance, when faithfully applied by ministers, and faithfully received by parents, are abundant-nay, great and important in every way. When children are baptized, they are thereby recognized as belonging to the visible church of God. They are, as it were, solemnly entered as scholars or disciples in the school of Christ. They are brought into a situation, in which they not only may be trained up for God, but in which their parents are bound so to train them up; and the church is bound to see that they be so trained, as that the Lord’s claim to them shall ever be recognized and maintained.
In a word, by baptism, when the administrators and recipients are both faithful to their respective trusts, children are brought into a situation in which all the means of grace, all the privileges pertaining to Christ’s covenant family, in a word, all that is comprehended under the broad and precious import of the term Christian education, is secured to them in the most ample manner. Let parents think of this, when they come to present their children in this holy ordinance. And let children lay this to heart, when they come to years in which they are capable of remembering and realizing their solemn responsibility.
This is why churches should be in the business of training up children through various means most notably through Christian schools, including children in worship, and catechism classes. All churches cannot do all these things. But the church, as well as the parents, have the solemn duty to train the children in the discipline and instruction of the Lord.