God's design for families is about flourishing. Throughout His Word, the key to cultural renewal was the family. Changing culture meant changing families, and changing families happened through the leadership of the home. The primary responsibility for discipleship in the home falls upon parents, and fathers are the ones called to take the lead in setting that culture.
In Nehemiah 8:13-18, Ezra and Nehemiah teach the heads of Jerusalem's families about how to observe the festivals proscribed in the Law of Moses. These had fallen into disrepair and hadn't been practiced faithfully for generations. These family leaders were called to teach the Law to their families, lead them in observance, and ultimately show their families that their true deliverance and shelter came from faithfully following the Lord. In the same way, God's design for dads is that they would teach their families to find shelter in Jesus Christ.