In Paul and the Faithfulness of God, NT Wright observes Paul's call to fellowship-- "Something is going on here. A new way of life is being attempted—by no means entirely discontinuous with what was there already, but looking at things in a new way, trying out a new path" (p. 4). 

This path is what we're discussing from Hebrews 13:1-3, going full-on family, Jesus-style.