Question
Why is it incorrect to say that Christ became "a human being" or "a man"?
Answer
Because Jesus Christ is the "God-man", and not the "Man-God". In other words, Christ is the divine Person of God the Word, the Second Hypostasis of the Holy Trinity, who "became flesh" (John 1:14) for the salvation of the world; He did not become "a human person". So there is no "second subject" in Christ.
In this sense, you could say that Christ is "a divine-and-human being", by virtue of the fact that the single Person of God the Word exists in two natures, His pre-eternal divine nature and His assumed created, human nature.
However, it must be stated clearly that God the Word did not appropriate "a human person" to Himself, as St. Cyril of Alexandria points out in his Second Letter to Nestorius: "Scripture does not say that the Logos united the 'prosopon' [person] of a man to Himself, but that He became flesh" (John 1:14).
As the single and unique divine Person of the divine Logos, He "became flesh", that is to say, He assumed the fullness of our human nature - a human body and a reasonable and spiritual human soul - and thus became the God-man.
And this is why we refer to Him as true and perfect God and true and perfect man: Jesus Christ is the One Hypostasis of God the Word who now, after the Incarnation, exists in His divine and human natures.
St. Gregory Palamas: The Son of God did not take a Human Person
"Since the only-begotten Son of God did not take a human person from us, but our nature, and made it new, being united with it in His own person,* does He not impart His grace to each person, and does each of us not receive the forgiveness of sins from Him?
How could this be otherwise, as He "will have all men to be perfectly saved" (cf. 1 Tim. 2:4), "bowed the heavens and came down" (cf. Ps. 18:9) for the sake of all and, having shown us the road to salvation in its entirety through His deeds, words and sufferings, ascended into heaven and drew believers thither?
He renewed the nature He received from us for our sake, and showed it to be sanctified and justified, and obedient in all respects to the Father by what He Himself did and suffered being united with it in His person. On the other hand, He has not merely renewed the nature of each of us who believe, but also our person, and granted us remission of sins through divine baptism, through the keeping of His commandments, through the repentance which He bestowed on the fallen, and through the communion of His own body and blood."
Saint Gregory Palamas: The Homilies, Homily 60, On Holy Theophany, p. 501.
*Italics mine.
DrCNV