This earthly family mirrors in many ways the divine family of the Theoi as not all of the Gods were related to each other with one remove (parent/child or sibling). In fact, the Gods adopted new Gods as they were discovered and (often) syncretized. The melding of the Greek and Egyptian Gods in Alexandria is an example of the process.
What does this mirroring imply for an earthly family? It implies that each family is more than just the sum of its blood relations as each member of that family will inevitably create bonds of adopted family with those outside the blood ties. And THIS makes all of mankind potentially one family.
It is because of this that we have to be careful of our attachments.