St. Athanasius insists that it was crucial for Christ's redemption of us that Christ both share in the divine nature and in the human nature: in the divine nature to unite us with God, and in the human nature in order to unite us with God. The bond of a common nature with us made his redemptive work applicable to us.
The idea that the common human nature is a genuine bond is a fruitful one. (A lot of science-fiction from the middle of the last century takes this bond to be important. Yes, the aliens of the stories are persons, but there is a special bond that human persons share. However, a number of science-fiction writers confused this special bond with some kind of human superiority to the aliens they populated their stories with. But that is mistaken, a mistake which we will avoid if we remember C. S. Lewis's discussion of two kinds of patriotism--the bad kind where one likes one's country because one thinks one's country is better and the good kind where one simply has affection for one's country and its institutions and culture.)
It is, however, tempting after Kant to see what is significant about us as not our humanity which integrally includes both the personal and the animal aspects of our existence, but just the personal aspects. If we see what is significant about us as just personhood, then Athanasius' account of why the Incarnation was needed loses some of its force. For if what is significant about us is personhood, then the second person of the Trinity already had personhood prior to the Incarnation. Admittedly that personhood was not precisely like ours--if St. Thomas is right, we can term the Logos and ourselves "persons" only by analogy. But nonetheless there is an analogy there, and the fleshly nature of the Incarnation becomes less clearly needed.
It is theologically important to hold on to the idea that we are not just persons. We are also animals. We are human beings with all that this entails. That is one reason why accounts that attempt to reconcile evolution with the divine plan by insisting that God only cared about producing persons, and left it to a chance he did not control whether these persons should be mammals or reptiles, biped or quadrapeds, and so on, are theologically mistaken. A part of the significance of the Incarnation is that our concrete enfleshment matters. The kind of persons we are is defined in large part by our flesh, and the kind of flesh we have is defined in large part by its aptness towards personal activity. Ignoring the concrete enfleshment is apt to lead us to philosophical error, such as the error of those who think that there are two co-located beings in front of this computer, one a person and the other an animal, an error that leads to moral mistakes on issues like abortion and euthanasia.
What is this commonality of nature that all of humans have and which St. Athanasius thought so important? Platonists will say it is our common participation in a single thing, the Form of Humanity. Aristotelians will say that it is our possession of numerically distinct essences, which are, nonetheless, qualitatively the same. The Platonic story fits somewhat better with St. Athanasius' account, but both accounts provide an ontological basis for the commonality of nature.
Christ, having reconciled us human beings with God will also re-integrate our nature, bringing the animal and the personal together, when he transforms us in the resurrection, completing his new creation in us. Blessed be his name!
The Word became flesh. Let us bend the knees of our body and of our soul before him as we celebrate with joy this jarring truth.