God did not create us alone. We all arrive on this earth into a family. Just as each of us is unique, each family is also unique--different blends of ages, genders, personalities, relationships. Extended families are part of the glue that builds societies.
Families include a variety of relationships, not all predictable by bloodlines. Besides the obvious parent/child and sibling relationships, some of them closer than others, there are the extended connections--aunts, uncles, cousins, even in-laws. Cousins are often special--close enough to share events and relatives, but often with different experiences of the shared relatives, which makes for great conversations.
In the Christmas story, it is interesting that the angel that came to Mary told her about Elizabeth's miracle, and that Mary's reaction to the news was to go be part of it. It's very possible that because Elizabeth had not had children of her own that she had already "adopted" this younger cousin to build a special relationship with. Being an only girl in my own family, I was blessed to have an aunt and a sister-in-law who had only boys take me under their wings, and several childless friends of my parents became "honorary aunts."
If you look at this story carefully, we notice that Elizabeth was six months along in her pregancy when Mary came and stayed for three months, so it is possible that Mary was there when John was born--or that she slipped out at that time to not call attention to herself.
We do see that family gathered to celebrate this birth. This is part of the way families are created--there are landmark events that gather folks to share and touch base with each other; births, marriages, deaths. Jesus' first miracle was at a wedding, at Cana of Galilee. We don't know whose wedding, but Mary was close enough to the host family to be concerned about the wine situation. We see Jesus often connecting people in family-type gatherings, and many of the stories He told are about weddings and banquets. The last family-type event we see Jesus involved with was Lazarus' death--which He turned from a funeral to a miracle.
As Christmas approaches, let us remember that not only did God give us the gift of His Son (and note that He describes Jesus in a "family" context) but also an opportunity for us to connect and share with our own families--immediate family, extended families, our church families, our communities, and layered all the way out to God's extended family around the world.