Why is parting sorrowful?

After spending a week or so together for Christmas, most of my children had to get back to school and work - to get on with their lives. I want them to be independent, but I still wish they didn't have to go away. Why can't we be entirely happy when they leave? Why are we made like this?

The day three of my children left I watched the DVD "The Return of the King" with one of my sons. Now I have stuck in my head the music played in the sad scene where Gandalf, Bilbo, and Frodo leave their friends.