Why is Jesus the Son called the Father in Isaiah 9:6? In providing this answer with respect to recognizing the Trinity in the Old Testament, I noticed that Jesus is called the Father which could be confusing when trying to understand the Trinity. In what sense is Jesus the Father but certainly not the Father?


  For to us a child is born, to us a son is given, and the government will be on his shoulders. And he will be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace. (NIV Isaiah 9:6)


Please do not answer unless your answers uphold the doctrine of the Trinity. I do not want the debate about the trinity to confuse the question. The answer must assume the Trinity is true, that is the Father, Son and Holy Spirit are equal yet different persons that share the same single divine nature and therefore are called the One and true God.
And why is he called Counselor? These are adjectives used to describe/praise him. These are metaphorical descriptions.

He is also a brother and a son - 


  Mat 12:48 He replied to him, “Who is my mother, and who are my brothers?” 49
  Pointing to his disciples, he said, “Here are my mother and my
  brothers. 50 For whoever does the will of my Father in heaven is my
  brother and sister and mother.”


He is both, the son of David and Lord of David - 


  Mat 22:42 “What do you think about the Messiah? Whose son is he?” “The
  son of David,” they replied. 43 He said to them, “How is it then that
  David, speaking by the Spirit, calls him ‘Lord’? For he says, 44 “‘The
  Lord said to my Lord:“Sit at my right hand until I put your enemies
  under your feet.”’


I think His description as an everlasting father is supposed to illustrate a point that He will watch over and protect His disciples whom he considers as His own children - 


  John 14:18 I will not leave you as orphans; I will come to you.


Edit: 
I would like to make an addition. 

This question reveals one of the mistakes that non-trinitarians make. Attempting to define God in human terms and concepts.

The concept of father, mother, brother, sister did not exist before God invented the family unit. It would've been meaningless to call someone your brother before Adam and Eve had sons.

God who created these concepts, is not defined/limited by these. He is above these concepts and yet he is the perfect fulfillment of them. He is not the brother of anyone. Yet he is the perfect model/example of a good brother.

I am a sister. I had no choice, I was given this role. But He voluntarily takes upon these roles for our sakes, becoming our friend, counselor, brother, father, shepherd, and everything else it takes for the expression of His love towards us.