We're pulling a lot of our material for this lesson from St. Athanasius. I have to say this up front - Athanasius is my boy. Not only does he weave together a magnificent treatise on the incarnation, but you can tell that he sincerely believes it too. And not only that, he lives by it. He lives as if he actually believes in the incarnation. That means that he wasn't intimidated by emperors, heretics, or anyone else. He believed in Jesus, and for him, that was enough.
Here's Athanasius in a nutshell. First, Christ's incarnation was a sacrifice. He stooped down to us in order to heal ("salvation" means "healing) us. Second, Christ abolishes death. His work in life and on the cross and at the empty tomb is the final defeat of death. Lastly, just as God became man, our hope is that we become like God.
I hope you can see the progression here. It really is quite beautiful. The incarnation is not about shepherds, angels, wise men, and silly children's Christmas pageants. Christmas is about our salvation. Christmas is about the incarnation. Christmas is about God's sacrifice for us, so that we can live with God.