Notice that fathers specifically are addressed in the passage: "And, fathers, do not nag your children lest they lose heart" (Col 3:21). Fathers must not nag (Col 3:21) or anger (Eph 6:4) their children. This means that a father must make sure that his word is effective as soon as he speaks it. When a father issues a command, he must ensure — in a firm, respected way rather than by a nagging or domineering manner — that his word is honored.
We fathers are to imitate God our Father. It is beneath God the Father's dignity to nag us. The Father commands us firmly and directly, yet does so in a way that we never forget He loves us. This is where the father must employ hands-on "training and instruction befitting the Lord" (Eph 6:4). A father is not to "nag" his child ten times to take out the trash (Eph 6:4). If his child doesn't comply when the father requests, the father drops what he is doing. He teaches, accompanies, or disciplines his child. Firmly, yet lovingly, he ensures that his command is followed. Like God our Father, without yielding our dignity and authority, we fathers "train our children to obey their parents in the Lord" (Eph 6:1) and "honor their father and mother" (Eph 6:2).
It's tempting as fathers to want to take a shortcut and dominate our children. Yet if we take shortcuts, so will our children, for they do what they see their fathers do (see Jn 5:19). A father's vocation, in imitation of God the Father, is to be personally and lovingly involved with his children (see Jn 5:20). When we train our children properly, they "will not swerve from it" (Prv 22:6).