The core of the gospel is God's promise that forgiveness and relationship to Him comes to those who embrace the sending of his Son as a gift for us. This presence gifts us with his presence within our lives when we recognize we cannot enable ourselves to live as God designed us to live.
When God sent a child (His Son) to represent him within our/his world, he was making a statement about our need for him. When God took on humanity in His Son, he also took on a representation of the importance and uniqueness of being human and of being connected to God. So it is not merely Jesus' presence on earth that is important to the Christmas story; it is what he taught and represented to us about what God desires from us as Creator.
The examples Jesus praised in his life where of people who did not think they were entitled to blessing but who knew it had to be received as a work of God's grace and mercy. Just consider the centurion who said I know your authority and I am not worthy for you to come under my roof, but I believe in what you can do. He was affirmed by Jesus. Or consider the sinful woman who while saying nothing, simply wept at Jesus' feet in appreciation for the forgiveness he offered. Jesus affirmed her act. Or think of the prodigal who returned to the Father knowing he was not worthy to be a son only to have the Father receive him back as a son. Jesus illustrated how God receives the lost who come back to Him seeking nothing but what he can offer. Or consider the tax collector who simply said while beating his breast, "Have mercy on me, God." Jesus said this was the attitude God justified. Or consider the Canaanite woman who said even the crumbs from God are good enough. Jesus affirmed her humility by granting her request.
None of this presumes on God, but turns in trust to him. The birth of Jesus is heaven's call and cry to listen to what God has done for us through Jesus. We do not get to God the old fashioned way--by earning it. We get to God by receiving his forgiveness and the Spirit he offers to come into our lives to enable us to relate to Him. We come humbly, seeking the mercy and grace God freely gives and believing he will do it by giving us life. We come grateful that God cares enough about us to take us on himself. So the birth of Jesus is not just another nice story among many that touches our hearts. It is a unique event that seeks to transform our hearts and call us to sit at God's feet.
Christmas calls us to listen to how to live life as God designed it to be lived. In other words, the story of Jesus' birth is not about its start, but about its coming and why he even bothered to do it. To understand Christmas, one needs to look at Jesus' life and teaching, a teaching that calls us to draw near to God and his grace, knowing that we cannot do for ourselves (no matter how hard we may try) what God is able to do as he gave of himself for us.