The heart of the Christmas message is that there, lying in the manger, lies God in human flesh. In a word, then, Christmas is about the Chalcedonian Definition (451 A.D), or rather, the other way round. If you’ve never read it, here it is:
Therefore, following the holy fathers, we all with one accord teach men to acknowledge one and the same Son, our Lord Jesus Christ, at once complete in Godhead and complete in manhood, truly God and truly man, consisting also of a reasonable soul and body; of one substance with the Father as regards his Godhead, and at the same time of one substance with us as regards his manhood; like us in all respects, apart from sin; as regards his Godhead, begotten of the Father before the ages, but yet as regards his manhood begotten, for us men and for our salvation, of Mary the Virgin, the God-bearer; one and the same Christ, Son, Lord, Only-begotten, recognized in two natures, without confusion, without change, without division, without separation; the distinction of natures being in no way annulled by the union, but rather the characteristics of each nature being preserved and coming together to form one person and subsistence, not as parted or separated into two persons, but one and the same Son and Only-begotten God the Word, Lord Jesus Christ; even as the prophets from earliest times spoke of him, and our Lord Jesus Christ himself taught us, and the creed of the fathers has handed down to us.
As technically precise as it is, many have questioned and wondered whether in defining, or at least laying down some boundaries for how to think about Christ, the Fathers have departed from the simpler, or clearer language of Scripture. The worry is that in the process of parsing of things metaphysically, through the conceptualities of Greek philosophy and terminology, the Biblical Gospel has been lost.
Herman Bavinck answers this sort of charge at length, beautifully summarizing his findings in this brief passage:
Thus God and man are united in Christ. While Scripture does not speak the language of the later theology, materially it contains what the Christian church confesses in its doctrine of the two natures…For according to Scripture, the Word that was with God and was himself God became flesh (John 1:14). He who was the reflection of God’s glory and the exact imprint of God’s very being has become partaker in our flesh and blood and like us in all things (Heb. 1:3; 2:14). God sent his own Son into the world, who was born of a woman (Gal. 4:4). Though existing in “the form of God,” he “emptied himself, taking the form of a slave” (Phil. 2:7). From the fathers, according to the flesh (κατα σαρκα), comes the Messiah, who is over all, God blessed forever (Rom. 9:5). Though the image of the invisible God, the firstborn of all creation, he is nevertheless also the firstborn from the dead (Col. 1:13–18); though son of David, he is simultaneously David’s Lord (Matt. 22:43); even though walking about on earth, he still continues to be “in the bosom of the Father” (John 1:18), “the one who is in heaven” (John 3:13), and existed before Abraham was (John 8:58); in a word, the fullness of deity dwells in him bodily (σωματικως, Col. 2:9). Every moment in Scripture, divine as well as human predicates are attributed to the same personal subject: divine and human existence, omnipresence and [geographical] limitation, eternity and time, creative omnipotence and creaturely weakness. What else is this but the church’s doctrine of the two natures united in one person?
–Reformed Dogmatics Volume 3: Sin and Salvation, pg. 298-299
It must not be lost to sight that all of this theologizing is done to preserve the crucial Gospel truth: it is God who is with us, to save us in Christ. Calvin comments on Matthew 1:23:
The phrase, God is with us, is no doubt frequently employed in Scripture to denote, that he is present with us by his assistance and grace, and displays the power of his hand in our defense. But here we are instructed as to the manner in which God communicates with men. For out of Christ we are alienated from him; but through Christ we are not only received into his favor, but are made one with him. When Paul says, that the Jews under the law were nigh to God, (Ephesians 2:17,) and that a deadly enmity (Ephesians 2:15) subsisted between him and the Gentiles, he means only that, by shadows and figures, God then gave to the people whom he had adopted the tokens of his presence. That promise was still in force, “The Lord thy God is among you,” (Deuteronomy 7:21,) and, “This is my rest for ever,” (Psalm 132:14.) But while the familiar intercourse between God and the people depended on a Mediator, what had not yet fully taken place was shadowed out by symbols. His seat and residence is placed “between the Cherubim,” (Psalm 80:1,) because the ark was the figure and visible pledge of his glory.
But in Christ the actual presence of God with his people, and not, as before, his shadowy presence, has been exhibited. This is the reason, why Paul says, that “in him dwelleth all the fullness of the Godhead bodily,” (Colossians 2:9.) And certainly he would not be a properly qualified Mediator, if he did not unite both natures in his person, and thus bring men into an alliance with God…
For it cannot be denied, that this name, Immanuel, contains an implied contrast between the presence of God, as exhibited in Christ, with every other kind of presence, which was manifested to the ancient people before his coming. If the reason of this name began to be actually true, when Christ appeared in the flesh, it follows that it was not completely, but only in part, that God was formerly united with the Fathers.
Hence arises another proof, that Christ is God manifested in the flesh, (1 Timothy 3:16.) He discharged, indeed, the office of Mediator from the beginning of the world; but as this depended wholly on the latest revelation, he is justly called Immanuel at that time, when clothed, as it were, with a new character, he appears in public as a Priest, to atone for the sins of men by the sacrifice of his body, to reconcile them to the Father by the price of his blood, and, in a word, to fulfill every part of the salvation of men. The first thing which we ought to consider in this name is the divine majesty of Christ, so as to yield to him the reverence which is due to the only and eternal God. But we must not, at the same time, forget the fruit which God intended that we should collect and receive from this name. For whenever we contemplate the one person of Christ as God-man, we ought to hold it for certain that, if we are united to Christ by faith, we possess God.
This is a staggering and astonishing reality. If we are united to Christ, “by faith, we possess God.” This is the mystery, the miracle, and the grace of Christmas: in Christ, God truly gives himself to sinners for their salvation and joy.
Soli Deo Gloria