Orthodox teaches that Jesus assumed the full human nature. Why is it necessary that he is fully human?
Historically, the position of the church on Christology has been explained as "hypostatic union, meaning that Jesus was fully God and fully man). In the late 300s, Nestorius taught that Jesus' natures were separate. The problem comes when you consider salvation.
The problem with Nestorianism is that it threatens the atonement. If Jesus is two persons, then which one died on the cross? If it was the "human person," then the atonement is not of divine quality and thereby insufficient to cleanse us of our sins.
Put another way, satisfaction is untenable, because the sacrifice cannot stand in for the crime.
The opposite error was Eutychism or Monophysitism which ignores the human nature and is not supported by Scripture. Related forms would be if God the Son merely appeared to be human (the heresy of Docetism or Apollinarism.
Who, being in very nature[a] God, did not consider equality with God something to be used to his own advantage; 7 rather, he made himself nothing by taking the very nature[b] of a servant, being made in human likeness. 8 And being found in appearance as a man, he humbled himself by becoming obedient to death— even death on a cross!
or Hebrews 4:15:
For we do not have a high priest who is unable to empathize with our weaknesses, but we have one who has been tempted in every way, just as we are--yet he did not sin.
that emphasize Christ's ability to sympathize with our humanity. Absent a human nature, that would be a lie.
Liberals, like Dr. Martin Luther King, Jr. go further with this. As he writes:
Where then can we in the liberal tradition find the divine dimension in Jesus? We may find the divinity of Christ not in his substantial unity with God, but in his filial consciousness and in his unique dependence upon God. It was his felling of absolute dependence on God, as Schleiermaker would say, that made him divine. Yes it was the warmest of his devotion to God and the intimacy of his trust in God that accounts for his being the supreme revelation of God. All of this reveals to us that one man has at last realized his true divine calling: That of becoming a true son of man by becoming a true son of God. It is the achievement of a man who has, as nearly as we can tell, completely opened his life to the influence of the divine spirit.
In his moral influence understanding, his human nature that adopted a divine one required as a starting point a human one.
Hypostatic union is define at Chalcedon. But the idea has existed before that.
What has not been assumed has not been healed
St. Gregory of Nazianzus, Epistle 101:32.
Against Apollinarius, Gregory argued that if Christ had not been "endowed with a rational mind, how could he have been a man?" Epistle 101:34. Here, we see how the unity of Christological thought from First Constantinople (381) to Third Constantinople (681) is complementary to each other. Without two wills Christology there is no hope for salvation. Unless the Logos has His own human mind or will, His incarnation achieved nothing. By assuming a human mind He redeemed our nature completely. Our flesh is redeemed because He clothed Himself with a human flesh. Our soul is redeemed because He assumed a human soul. Our will is redeemed because He assumed a human soul with rational mind. This is why He has made His dwelling among mankind. Following Ss. Irenaeus and Athanasius, Gregory continue to defend Theosis. Becoming a man, Christ gave us the possibility of becoming deified.
Let us seek to be like Christ, because Christ also became like us: to become gods through Him since He Himself, through us, became a man. He took the worst upon Himself to make us a gift of the best
St. Gregory of Nazianzus, Orations 1:5.
Unless God became man we won't be able to be deified, partaking of the divine nature. This is why Christological belief in the hypostatic union include a belief that the Logos became flesh, assuming a complete human nature to redeem our nature. That is the Gospel, He became man so that we might become like Him.