Why do adherents to Hypostatic Union believe that God the Son (Jesus) must be fully Human? 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.

In any Satisfaction theory of atonement, the 'victim' that satisfies God's wrath must be a viable substitute.  As the Christian Apologetics &amp; Research Ministry (CARM) writes:


  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.

Monophysitism in general was considered heretical because it denies either the divine or the human nature. Biblically, this negates key passages such as Philippians 2:5-11:


  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.