Earthly institutions are fundamentally separate from heavenly ones, and the family is no exception to that rule. Because none of them are eternal, none of them may be allowed to become idols, however good they are in their place.
Child-rearing has changed a great deal since Paul’s day, even as Paul himself pushed against the household codes of his own society to put the emphasis squarely on the Lord. The relationship of God the Father to the Son is the true pattern for every parent and child.