An architect knows where all the doors in a house will lead because he designed it. That is why man-made religions can seem plausible, being the product of human imagination. That is also why the fact that Christ is a divine reality, or "Person," while having two natures, challenges human understanding, because it is not a human invention.
In these days of Christmas, a good way to avoid reducing the Incarnation's mysterious meaning to simple expressions of goodwill and Dickensian jollity is to read the Athanasian Creed, focusing on the lines: "Although He is God and Man, He is not two, but one Christ. And He is one, not because His divinity was changed into flesh, but because His humanity was assumed unto God. He is one, not by a mingling of substances, but by unity of person."
A sure way to get the Incarnation wrong is to try to use mere human imagery to explain it. One recent attempt, with the best of intentions, was to make an analogy between the two natures of Christ and the mixed races of mestizos who are part European and part American Indian.
This echoes the mistake of the monk Eutyches (d. 454), who imagined the divinity and humanity of Christ as fused into a sort of homogenized third reality, half God and half Man.
Not to make light of such a serious mistake, but it reminds one of the Gilbert and Sullivan operetta Iolanthe, named for a woodland fairy who bears a son, Strephon, fathered by a mortal man. Strephon's problem is that he is half sprite and half human, so when he tries to fly through a keyhole, his human legs get stuck.
There were even bishops who did not want to think more deeply than Eutyches, although he had been condemned as a heretic in 448, and they rehabilitated him at a bogus "robber" Council of Ephesus in Turkey.
Pope Leo (known to history as "the Great") appealed from Rome to the venerable lady Pulcheria, empress in the Byzantine half of the Roman Empire, who at the time was regent during the minority of her brother Theodosius II, asking her to summon another council.
During the third session of that assembly in Chalcedon, a letter from the pope was read, defining the true mystery of the Son of God, and the bishops cried out in chorus: "This is the Faith of the Fathers, this is the Faith of the Apostles. We all believe, the orthodox believe thus. Those who do not believe thus are excommunicated. Peter has spoken through the mouth of Leo."
At Christmas we remember the words Peter heard from the Master, who was once cradled in Bethlehem: "[F]lesh and blood has not revealed this to you, but my Father who is in Heaven." (Matthew 16:17)