It is often asserted by Christian trinitarians when the words ‘Son of God’ is used for Jesus in the New Testament, then that proves he is God himself. Trinitarians hold to the belief that the declaration that Jesus is the ‘Son of God’, means he is God the Son, a member of the Trinity. However, Jesus (p) never claimed to be a member of the Trinity. The Trinity concept was build up centuries later by the Church Fathers. I will now show passages from Mark’s Gospel where the words ‘Son of God’ is used, as Mark is the earliest Gospel to be written according to Scholars.
Mark 1:1 – “The beginning of the good news of Jesus Christ, the Son of God.”
Mark 3:3 – “You are the Son of God!”
Mark 15:39 – “Surely this man was the Son of God!”
As you have read the passages, question arises are the words ‘Son of God’ unique to Jesus alone? The answer is no! To be called the ‘Son of God’ does not mean that Jesus shares God’s nature. Son of God, the term has been used many times in Old Testament, but nowhere does it imply that the person shares YHWH’S nature. Here are the following passages where the term is used:
(1) Genesis 6:4 The Nephilim were on the earth in those days, and also afterward, when the sons of God came in to the daughters of men, and they bore children to them. Those were the mighty men who were of old, men of renown. Genesis 6:4
(2) Exodus 4:22 Then say to Pharaoh, ‘This is what the LORD says: Israel is my firstborn son.
(3) Deuteronomy 14:1 “You are the sons of the LORD your God. You shall not cut yourselves or make any baldness on your foreheads for the dead.
(4) Deuteronomy 32:8 When the Most High gave to the nations their inheritance, when he divided mankind, he fixed the borders of the peoples according to the number of the sons of God.
(5) Deuteronomy 32:19 The LORD saw this and rejected them because he was angered by his sons and daughters.
(6) 2 Samuel 7:14 I will be his Father, and he shall be My son. If he commits iniquity, I will chasten him with the rod of men and with the blows of the sons of men.
(7) 1 Chronicles 17:13 I will be his father, and he will be my son. I will never take my love away from him, as I took it away from your predecessor.
(8) 1 Chronicles 22:10 He is the one who will build a house for my Name. He will be my son, and I will be his father. And I will establish the throne of his kingdom over Israel forever.’
(9) 1 Chronicles 28:6 He said to me: ‘Solomon your son is the one who will build my house and my courts, for I have chosen him to be my son, and I will be his father.
(10) Psalms 29:1 A Psalm of David. Ascribe to the LORD, O sons of the mighty, Ascribe to the LORD glory and strength.
(11) Psalms 82:6 “I said, ‘You are “gods”; you are all sons of the Most High.’
(12) Psalms 89:6 For who in the skies is comparable to the LORD? Who among the sons of the mighty is like the LORD
(13) Psalms 89:26-27 He will say to me, ‘You are my Father and my God, as well as the mighty rock where I am safe.’ “I have chosen David as my first-born son, and he will be the ruler of all kings on earth.
(14) Isaiah 43:6 I will say to the north, ‘Give them up!’ and to the south, ‘Do not hold them back.’ Bring my sons from afar and my daughters from the ends of the earth.
(15) Jeremiah 31:9 They will come with weeping; they will pray as I bring them back. I will lead them beside streams of water on a level path where they will not stumble, because I am Israel’s father, and Ephraim is my firstborn son.
(16) Daniel 3:25 He answered and said, Lo, I see four men loose, walking in the midst of the fire, and they have no hurt; and the form of the fourth is like the Son of God.
(17) Hosea 1:10 Yet the number of the sons of Israel Will be like the sand of the sea, Which cannot be measured or numbered; And in the place Where it is said to them, “You are not My people,” It will be said to them, “You are the sons of the living God.”
(18) Hosea 11:1 “When Israel was a child, I loved him, and out of Egypt I called my son.
Reading the above passages shows that Israel as a whole is God’s sons and daughters. Angels are also God’s sons. It’s quite clear reading all the above verses that being the ‘Son of God’ did not and was never understood to denote that the person is sharing God’s nature. If Trinitarians still insist that the term ‘Son of God’ means ‘divinity’. Then they have to be consistent and apply the same for all the other passages when ‘son of God’ is used in the Old Testament. If we go by Trinitarian logic, then all the people in the Old Testament are equally God just as is Jesus is (as claimed by Christian Trinitarians) in the New Testament. When the term ‘son of God’ is used in a Jewish sense, it means someone who is a righteous person. It is used for the nation of Israel or a person who has a close relationship with God Almighty. Let’s now present some Scholarly evidences on the term ‘Son of God’.
The Oxford Dictionary of the Jewish Religion says:
“Son of God, term occasionally found in Jewish literature, biblical and post-biblical, but nowhere implying physical descent of a human from the Godhead. In general terms, the Jewish people are referred to as ‘the children of the Lord your God’ (Dt. 14:1; cf. Ex. 4.22 and Hos. 11.1), in relation to the concept of the fatherhood of God. Genesis 6.2 mentions the ‘sons of God’ who intermarried with the daughters of man; the origins of the phrase here presumably reflect ancient Near Eastern polytheistic assumptions. It came to be taken as a reference to angels (also in Ps, 82.6), and it used in this sense in the Berikh Shemei prayer (in its Aramaic form) from the Zohar, which is recited in some rites at the opening of the ark of the covenant in the synagogue. The application of the term to Jesus by the early Christian church was probably a combination of the metaphorical use of the term in Jewish apocryphal literature (e.eg., Wisdom of Solomon. 2.18) with the more material conception of the divine man (theios aner) common in surrounding cultures of the day. When used by Rabbis, the reference was to Israel or to human beings in general. …”
Eerdmans Dictionary of the Bible
“Son of God
A person or people having close relationship with God; in the NT a designation of Jesus. The Lord promised through Nathan that David’s ancestor would be ‘a son to me’ (2Sam. 7:14; 1 Chr. 17:13; 22:10; 28:6), and other texts call the King the Lord’s son (Ps. 2:7; cf. Isa. 9:6-7 [MT 5-6]) and firstborn (Ps. 89:27-29 [28-30]). Several passages call the Lord the ‘father’ of Israel (Deut. 32:6; Isa. 64:8 ; Jer. 31:9), and others refer to Israel or Ephraim as the Lord’s ‘son’ (Exod. 4:22-23; Jer. 319; Hos. 11:1). The people can be called the Lord’s sons and daughters (Deut. 32:19; Isa. 43:6; Hos. 1:10 [2:1].
Intertestamental Jewish sources call the angels sons of God (Wis. 5:5) and identify the suffering righteous man as God’s son (Wis. 2:16-18; Sir.4:10), and several texts from the Quran, especially the hotly debated Aramiac text 4Q246, provide enigmatic evidence concerning the term ‘son of God’ (Cf. also 4QFlor 1:11-13; 1QSa 2:11). The Greco-Roman world bestowed the title Son of God on Caesar. …” 
Reverend Thomas P. Rausch, S.J., Ph.D., who is the T. Marie Chilton Professor of Catholic Theology and professor of theological studies at Loyola Marymount University in Los Angeles, he writes:
“The earliest version of the Apostles Creed in Hippolytus Apostolic Tradition asks simply, do you believe in Christ Jesus, the Son of God? Referring to Jesus as God’s ‘only son’ is to use a biblical metaphor that has undergone a considerable development, even metamorphosis. In the Old Testament the title ‘son of God’ has a variety of meanings or usages. It could refer to the expected ‘son of David,’ the royal successor who God had promised to adopt (2 Sam 7:14; Ps 89:27), as we have seen. ‘Son of God’ was also used for the just man in the Wisdom tradition (Sir 4:10; Wisdom 2:16-20), for angels (Job 1:6; 2:1), and sometimes for the people of Israel collectively (Exod 4:22; Deut 14:1). The title Son of God was also used in other eastern religions for kings and wonder workers. None of these have the implication of divinity, nor do all of the appearances of this title in the New Testament. …” 
Charlene P. E. Burns is Associate Professor of Religious Studies at the University of Wisconsin-Eau Claire. She says:
“A brief look at the title Son of God is illuminating. Although we have no evidence that Jesus actually referred to himself as the Son of God, the phrase appears in the creeds and is central to Christian belief.
In the first century, people were not infrequently referred to as sons of God in order to indicate their status as somehow specially pleasing to or favoured by God. For example, mythological Greek heroes, like Hercules, were called sons of God. During Jesus lifetime, Caesar Augustus was commonly referred to as such, as were the rulers of Egypt. Within traditional Judaism the title was used in various ways, as we see in the Hebrew Scriptures. Angels are sons of God, according to numerous texts- Gen. 6:2-4 or Deut. 32:8, for example.
The king and other Israelites, even Israel itself, all received this title (2 Sa,. 7:14; Exod. 4:22). Intertestamental Judaism developed the theme further, and it is found in the writings of the Dead Sea Scrolls as well. Altogether then, it can be said that at the time of Jesus and during the early years of Christian formation, the term Son of God was widely known and used. To say that someone was the Son of God in antiquity seems to have meant something like ‘belonging to God.’ Given its somewhat common usage, it is not surprising that the term came to be associated with Jesus. We have no evidence to support the claim that, when first used to speak of Jesus, Son of God meant anything other than its then accepted meaning.
The title originally implied nothing like that Christian idea of Sonship as encompassing incarnational and Trinitarian themes. It was a metaphor used to indicate the special character of Jesus relationship to God. Although Jesus most likely did not consider himself to be the Son of God, it is feasible that he would have understood Israel and her people to be sons of God. As Conservative New Testament Scholar N. T. Wright says ‘I do not think Jesus [sat back and said] to himself, ‘well, I never! I’m the second person of the Trinity!
Some have argued that Jesus did have a sense of distinctive relationship to God, demonstrated by his reference to God as Abba or Father and his having taught the disciples that an appropriate form of prayer begins ‘Our Father….’ But this cannot be construed to mean that he thought of himself as the Son of God. It was common during Jesus lifetime for devout Jews to address God in prayer as Abba. His use of Abba in reference to God is not evidence for a theory of Jesus incarnational or pre-existent self-understanding. …” 
From the academic quotes, we see that ‘Son of God’ does not mean that the person referred to shares God’s nature. The evidences shown from the scholars is clear that, when someone was referred to as the ‘son of God’ – when it was used in the first century when Jesus (p) was alive, it only meant that the person was a righteous man or the person had a special relationship with God. The term was always used in a metaphorical sense. It was never used in a literal way. Paying close to the some of the scholarly statements, they also highlighted that the expression ‘son of God’ has ‘underwent considerable development’, they mean that the meaning for the term changed centuries down the line by Christians.
I hope Trinitarians from now on stop using the term ‘son of God’ as a claim for the divinity for Jesus. It is evident when the expression was used in the first Century when Jesus was alive, it only meant that he was a righteous man, a holy man and nothing more.
 The Oxford Dictionary of the Jewish Religion [Second Edition, Copyright 2011] by Adele Berlin page 698
 Eerdmans Dictionary of the Bible [Copyright 2000] By David Noel Freedman, Allen C. Myers page 1241
 I Believe in God: A Reflection on the Apostles’ Creed [Copyright 2008] By Professor Thomas P. Rausch page 67
 Divine Becoming: Rethinking Jesus and Incarnation [Copyright 2002] By Professor Charlene P. Embrey Burns page 34 http://www.metanexus.net/profile/charlene-p-e-burns