The family is a divine arrangement. Children are "an heritage of the Lord" (Psa. 127:3) having been given to their parents by God (Gen. 48:9).
Children do not ask to be born. Parents are responsible for bringing them into the world. It is a grave responsibility to give birth to a child. Even graver is the responsibility to train that child in the way he ought to go because every child has a soul that is destined to live somewhere for eternity.
They must provide for the material needs of their children (1 Tim. 5:8). Care must be exercised in this area because children can be given too much causing their sense of values to be distorted. Children need to learn the value of work. They need to learn about the cost of things.
They must "bring them up in the nurture and admonition of the Lord" (Eph. 6:4). Nurture is "the whole training and education of children (which relates to the cultivation of mind and morals, and employs for this purpose now commands and admonitions, now reproof and punishment" (Thayer's Greek-English Lexicon). The physical, mental, social, and spiritual training of the child must be according to the teaching of God.
They must not provoke their children to wrath (Eph. 6:4). The parallel text in Colossians 3:21 says children are not to be provoked "lest they be discouraged." There are a number of ways parents can produce wrath in their children.
They must set the right example before them. They must have a home where love, respect, and understanding prevails (Eph. 5:22-23; 4:32); where the Bible is studied and prayer is offered (2 Tim. 2:15; 1 Thes. 5:17); and where a high standard of morality exists (Titus 2:11-12; 2:4-5). They must also set a proper example in their service to the Lord and His church in attendance to services (Heb. 10:25; Matt. 6:33), respect for leaders (1 Tim. 5:17), reverence for worship (Ex. 3:5; Matt. 8:20), work (Phil. 2:12), and giving of one's means (1 Cor. 16:2; 2 Cor. 9:6-7).
They must teach them. Children must be taught the Bible (Deut. 6:7; Eph. 6:4; Titus 2:4-5); respect for parents (Rom. 1:30; Eph. 6:1-2), for older people (1 Tim. 5:1), and law officials (1 Tim. 2:1,4; Titus 3:1; 1 Pet. 2:17); to work (2 Thes. 3:10); proper use of money (Luke 16:11); about the permancy and sanctity of marriage (Heb. 13:4; Matt. 19:9); and the necessity of being faithful to the Lord by obeying His gospel (2 Thes. 1:7-9) and living a godly, faithful life (Rev. 2:19; Heb. 2:14).
The parent-child relationship, like all relationships, is recriprocal, i.e., it works both ways or it does not work. Children have responsibilities to their parents.
They must obey their parents (Eph. 6:1-4; Col. 3:20). God would have children be obedient to parents "in all things" (Col. 3:20) as long as the instructions of the parents do not violate the will of God.
They are to honor father and mother (Eph. 6:2). Honor involves such principles as love, respect, and obedience. Jesus applied this command to the idea of providing for parents when they become old and cannot provide for themselves (Mark 7:9,13; cf. 1 Tim. 5:4,8,16).
Parents: examine yourselves to see if you measure up to the standards God has set for you. Children: look at yourselves honestly and see if you are doing the will of Christ in respecting and obeying your parents.