Please read the passage before reading the commentary.
In the first century, Christians had to learn how to live among pagans. Their faith in Christ gave them a certain freedom in their manner of living, but such freedom at times was apt to raise some concerns with their pagan fellow citizens. They had relatives, friends and neighbors that were still pagan and who could be quite critical of the way Christians raised their families. Some of their neighbors felt that the way these Christians were living would be the death of civilization and life as they knew it.
Hence some precautious behavior was needed. Christian spouses had to respect pagan spouses and children still had to obey parents, even those who were pagan. Christian masters had to treat pagan slaves with kindness and Christian slaves had to obey their pagan masters. In other words, when life involved interacting with people of another faith, the Christians had to live at peace with those others.
Within the Christian family, parents should not relate harshly to their children, but they should teach their children how to fear God and grow in greater knowledge of the Lord.
Paul seems to have given the Christians he had written to earlier greater freedom, which he here seems to curtail, but Paul does not want the lifestyle of the Christians to threaten the peace of pagan-Christian relationships, as this lifestyle seemed to have quite a bit of pushback from the other inhabitants.
In our day, our manner of living must continue to draw others into communion with the Church which we proclaim in our manner of living.