The Bible speaks of several different groups of people: youth, young men/women, sons/daughters, and children.
Nowhere do we find corporate responsibility for children, nor an expectation for children to be instructed apart from the family unit.
For young men, the story is different. It should go without saying, but young men are men, not children. When is the transition from childhood to youth? When we put away childish things:
1 Corinthians 13:11 When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.
We do indeed find the young man singled out for instruction. Proverbs and Ecclesiastes both speak directly to him, to give him wisdom and understanding (Proverbs 1:1-4, Ecclesiastes 11:9-10, 12:1). Psalms calls upon him, with even little children, to praise the LORD (Psalm 148:12), and Joel tells us that he shall prophesy (Joel 2:28).
Children, not so. They are not given direct instruction, but are to receive it from their fathers, and along with them (Matthew 14:21, 1 John 2:13). They are by no means excluded (Matthew 18:1-6, 19:13-15, Mark 9:36, 10:13-16, Luke 18:15-17); it is expected that they will be present in the church (Acts 21:5). God even gave little children the special office of ordaining the Messiah (Matthew 21:15-16). But God has ordained their fathers for their instruction (Ephesians 6:4, Colossians 3:21, 1 Timothy 3:4-5,12, Titus 1:6). The whole of NT admonition directed at children is found in but two passages, and in each case only exhorts them unto obedience to their parents (Ephesians 6:1-3, Colossians 3:20). These 4 verses constitute the whole of “children’s church” in the NT.
In contrast, young men and women may receive direct rebuke (1 Timothy 5:1-2) and exhortation (Titus 2:6, 1 John 2:13-17), especially from those elder than themselves (Titus 2:4, 1 Peter 5:5).
God does observe our conduct even from our youth (Genesis 8:21, Proverbs 20:11), and expects children to walk uprightly. When they do not, he may bring it into judgment (2 Kings 2:23-24, Job 13:26, 20:11, 36:13, Psalm 25:7, Jeremiah 3:25, 22:21, 31:19, Isaiah 9:17). We are therefore admonished to flee youthful lusts (2 Timothy 2:22), and cleanse our way by taking heed thereto according to the word of God (Psalm 119:9). Therefore may we serve the LORD from our youth (1 Samuel 2:11, 1 Kings 18:12, Job 29:4, Psalm 71:5,17, Jeremiah 1:6-7, Matthew 19:20, Acts 26:4, 2 Timothy 3:14), even being an example of the believers (1 Timothy 4:12).
For this reason, fathers carry a tremendous responsibility for bringing up their children. When we turn to the OT, we find countless verses which stress the importance both of instructing our children (Genesis 18:19, Exodus 12:26-17, 13:14-15, Deuteronomy 4:9-10, 6:7, 11:18-21, 32:46, Joshua 4:6,22, Psalm 78:1-8, Isaiah 38:19, Joel 1:3), and of the consequences that are visited even on future generations when we do not (Exodus 20:5, 34:7, Numbers 14:18, 16:27, Deuteronomy 5:9, 2 Samuel 12:14, Job 5:3-4, 17:5, 20:10, 21:19, 27:14, Psalm 73:15, Jeremiah 2:9, 17:2, 31:29, 32:18, Hosea 4:6), or blessings when we do (Deuteronomy 1:36, 4:40, 5:29, 12:25,28, 17:20, Joshua 14:9, 2 Kings 8:19, 1 Chronicles 28:8, 2 Chronicles 30:9, Psalm 102:28, 103:17, 115:14, Proverbs 13:22, 20:7).
There is a clear principle of responsibility of the father for his children. There is no principle of corporate responsibility for children. We are not responsible for looking after the temporal or spiritual welfare of another’s child, except for the fatherless.
This is true even for a teacher in the church. Nowhere in either the Old or New Testaments is anyone other than a father charged with responsibility for instructing children.
Again, children were by no means excluded, it was commanded that they should hear the word of God as well as their parents (Exodus 34:23, Deuteronomy 31:11, 2 Chronicles 20:13, Ezra 10:1, Nehemiah 12:43, Joel 2:16, Zechariah 10:7,9). (Note that this is contrary to many models of Sunday school and youth group. Children were to be with the parents, hearing the word that they heard.)
But if any doubt the importance of the father-child relationship, Malachi 4:6 should settle it: Malachi 4:6 And he shall turn the heart of the fathers to the children, and the heart of the children to their fathers, lest I come and smite the earth with a curse.
Elijah the prophet would not come just to turn Israel to God, but to turn the hearts of the fathers to the children, and the children to the fathers. This is central to God’s work, his plan for Israel, and the full revelation of the Messiah. That is how important this created family bond is to God. A failure in it would cause God to curse the earth. This is his final words in the OT, the thought that he left his people with as he closed the OT canon. And nowhere in the NT do we find this pattern of parental responsibility changed; nay, we find it reinforced (1 Corinthians 4:14, Philippians 2:22, Hebrews 12:5, 3 John 1:4).
To summarize, in scripture we find children accompanying their parents to hear the word of God, but we do not find them receiving instruction apart from the family unit. Instead, their parents, specially their fathers, are charged with instructing them.
As children grow into youth and become young men and women, they eventually become autonomous, and receive their own instruction directly. There is a special need for the instruction of young men, and young women are to learn from the older women as well. This is in fact a part of the faith and sound doctrine.
But as long as a child is still receiving instruction from his father, this is not to be usurped. We may not find it forbidden, but the pattern laid out is clear and unflinching. All things are lawful unto me, but all things are not expedient.
Proverbs 29:21 He that delicately bringeth up his servant from a child shall have him become his son at the length.
There is a natural tendency to form a father-son bond with someone that you are delicately involved in bringing up. The resulting jealousies can easily undermine any positive outcome.
The Bible does not show us a pattern of parents delegating their responsibility to another. God does not want our children to be raised in the word. He wants us, their fathers, to raise them in the word.
Deuteronomy 6:7 And thou shalt teach them diligently unto thy children, and shalt talk of them when thou sittest in thine house, and when thou walkest by the way, and when thou liest down, and when thou risest up.
Deuteronomy 11:18 Therefore shall ye lay up these my words in your heart and in your soul, and bind them for a sign upon your hand, that they may be as frontlets between your eyes.
19 And ye shall teach them your children, speaking of them when thou sittest in thine house, and when thou walkest by the way, when thou liest down, and when thou risest up.
20 And thou shalt write them upon the door posts of thine house, and upon thy gates:
21 That your days may be multiplied, and the days of your children, in the land which the LORD sware unto your fathers to give them, as the days of heaven upon the earth.
God commanded each man to speak his words constantly in the ears of his children. The result was a blessing to both fathers and children.
When we have our children brought up in the word by others, we are not fulfilling this charge, and are forfeiting the full blessing, not only for ourselves, but for our children as well.
And again, look at the charge given. It is impossible for anyone but the parents of the child to fulfill it. Who else is going to be with the child while sitting in his house, walking by the way, lying down, and rising up—in all parts of life, at home and away, from morning till night? It is not possible to delegate this to somebody else, unless your children were to board with them. Thus, when we have our children instructed in the word primarily by others, not only are we failing to fulfill this charge, as said above, but moreover the charge is not being fulfilled at all. Firstly, because it was given to us and therefore it is ours alone to fulfill, and secondly, because unless we give up our children to another, no other is capable of fulfilling it. Again, the blessing is forfeited, not only for ourselves, but for our children.