The Gospel of John starts boldly! "In the beginning was the Word...and the Word was God...and the Word became flesh, and dwelt among us." John, the disciple who enjoyed the closest friendship with Jesus, gave us the most direct (and therefore the most startling) statement of Jesus' deity. Where some consider the Son of God as being distinct from God the Father, John's Gospel confronts us with God the Son.
This Incarnation, like the Trinity Itself, bypasses human intellect, leaving us uncomfortable with our inability to comprehend the Creator of all things "reducing" Himself to inhabit His virgin mother's womb. Offended by this apparent assault on our reasoning capabilities (as if we have some sort of right to equality with God), many of us invent false theologies that deny Jesus' deity...or badly distort it. Ever prideful, we demand a God that yields to our understanding--not one Who confronts us with our cognitive limitations.
Yet, John knew Jesus. He knew Him enough to be convinced that He was the very God of all creation. John had watched Jesus die on the cross, and only days later had eaten a fish breakfast with Him after His resurrection. The resurrection, more than any of the other miracles, verified Jesus' claim to be God. Intellect must always bow to fact, especially when fact defies intellect.
So we can best respond to the Incarnation, not by analyzing it or by trying to explain it, but by coming to the Lord in worship and adoration. With our intellects, we discern the overwhelming evidence for His resurrection, and from that point we reason that His claim to be God in the flesh is irrefutable. But then, trying to figure out how He could at once be fully God and fully Man must be set aside, letting us kneel at the manger.