All of the major days in the Church are feasts of Christ (Christmas, Epiphany, Easter, Pentecost, etc.), every month of the year has something for Mary (Mary Mother of God, the Annunciation, Our Lady of Guadalupe, etc.), and even Joseph gets two feasts, so why do we need a day for all three of them?
One of the big points of Christmas is the Incarnation, which is more than just the birth of Jesus. The Incarnation is, in a way, a throwback to Genesis, where God looks at everything he made, and finds it very good. And in spite of everything that each of us does to mess it up, God still finds it very good.
With the Incarnation, God shows that he doesn’t just find everything very good when seen from a distance. God steps into creation to be one of us, and makes it personal.
With the Holy Family, it's clear that God doesn’t just find someone who is fully God and fully man (Jesus) good, or someone who was born free from original sin (Mary) good, but that God also finds ordinary people who try to do it on their own and who get it wrong (Joseph) good as well. God finds each of us very good, and he finds us very good together.