I have seen some take this verse to mean men must apply a heavy, disciplinary hand in dealing with their family. But Jesus called them unto him and said, Ye know that the princes of the Gentiles exercise dominion over them, and they that are great exercise authority upon them. Jesus tells us in Matt. God expects his people to be humble servants. Fathers provoke not your children to wrath but bring them up in the nurture and admonition of the Lord.
Nurture comes from the Greek word paideia, meaning, tutorage, education or training.
A father is to teach, educate and train his children in the admonition of the Lord. The word admonition comes from the Greek word nouthesia, meaning calling attention to by mild rebuke or warning. Fathers, therefore, aren't to jump down their children's throat when they make a mistake, but are to rebuke and warn the child. It is a Father's responsibility to educate their children in the way of life God would have us all lead, calling their attention to the mistakes they make and rebuking them when necessary. A child who is brought up in the truth of God will have a sound foundation that will last him throughout life.