The Scriptures make this truth clear in the following passages:
John 1:1, 14; John 10:30; I John 5:20; I Tim. 2:5; Phil. 2:6; Gal. 4:4; Phil. 2:7; Heb. 2:14, 16-17; Heb. 4:15; Luke 1:35; Rom. 9:5; Col. 2:9; Heb. 7:24-25
The medieval theologian Thomas Aquinas used this terminology: "It is more proper to say that a divine person assumed a human nature, than to say that a divine nature assumed a human nature".
But why is this the case?
The Divine nature cannot be said to have assumed a human nature, because this would entail that the whole Godhead rather than just the Eternal Son, would have been united to human nature. The whole Godhead would have become incarnate. We only read in Scripture, however, that it was the divine essence of the Son which was united to man's nature.
The Divine nature cannot be said to have assumed a human person. If this was so there would have been a fourth person in the Godhead. Rather we understand that His human nature assumed a personality only in union with the Eternal Son. A human nature was assumed rather than a human person because he identified with what was common to that nature and not was particular to individuals. Thus, it was necessary for him to experience the hunger, thirst, grief, pain, weariness etc. that was common to human nature but not necessarily the diseases which only afflict individuals.
The Eternal Son cannot be said to have assumed a distinct human person because the human nature would have then belonged to that person and not to the Eternal Son.
The Eternal Son rather than the Father or Spirit must have assumed a human nature because there would then be two Sons in the Trinity. It was more fitting that the Eternally begotten son should be the one through whom the adoption believers as sons should be accomplished (Gal. 4:4-7).
The Word was made flesh by a personal action - he took human nature to Himself. He did not cease to be what he was before rather he added a nature to His person.