υἱὸς τοῦ θεοῦ (huios tou Theos)

In some translations, this Greek phrase has been translated to "Son of God."

However, in the context given - that of a certain relationship with God, “son” would be a mistranslation. While the Greek word υἱός (huios) can indicate a relationship of offspring (father/son), this is only in a limited or restricted sense. According to Thayer’s lexicon:
"in a restricted sense, the male offspring (one born by a father and of a mother)"
With respect to the context in which Jesus was speaking, Thayer's lexicon describes the usage of the word υἱός (huios):
"used to describe one who depends on another or is his follower - of teachers - i.q. pupils."
Thayer's lexicon further describes the meaning of this word in the contexts of devotion:
"one who is connected with or belongs to a thing by any kind of close relationship."
"instructed in evangelical truth and devotedly obedient to it"
"one to whom anything belongs"
"those to whom the phrophetic and covenant promises belong"
"The Jews called the Messiah υἱὸς τοῦ θεοῦ pre-eminently, as the supreme representative of God"
Thus we would more appropriately translate the phrase υἱὸς τοῦ θεοῦ within the definition given to it by those from whom the phrase had its origin:

"Servant of God" - when the context is general, related to one who is devoted to the Supreme Being.

"Representative of God" - when the context is specific and reverential, such as when referring to Jesus, who is representing God.

This later usage is consistent with Jesus' own statements, such as:
"For I have come down from heaven not to do my will but to do the will of Him who sent me. (John 6:38)
“My teaching is not my own. It comes from the One who sent me." (John 7:16)
The concept that ecclesiastical sectarians have claimed, of God begetting an exclusive son does not agree with scripture, nor with practical reality.

As for the representation that Jesus is God's exclusive son - why would God only beget one son? Would the Supreme Being, the Controller of all creation, somehow be limited in His ability to beget children? Most men can theoretically beget tens if not hundreds of children in their lifetime. And we are saying that the Supreme Being can only beget one person? Is God now impotent? Such a notion is absurd.

Such a notion also contradicts other verses elsewhere in scripture. We find many verses utilize refer to multiple devoted children of God, who were servants of God and sometimes acted as God's representatives:
When men began to increase in number on the earth and daughters were born to them, the sons [בֵּן (ben)] of God saw that the daughters of men were beautiful, and they married any of them they chose. (Genesis 6:1-2)
The Nephilim were on the earth in those days — and also afterward — when the sons [בֵּן (ben)] of God went to the daughters of men and had children by them. (Genesis 6:4)
[Jesus speaking] “Blessed are the peacemakers, for they will be called sons [υἱός (huios)] of God.” (Matthew 5:9)
...Adam, the son [υἱός (huios)] of God. (Luke 3:38)
[John, speaking of Jesus] Yet to all who received him, to those who believed in his name, he gave the right to become children [υἱός (huios)] of God. [John 1:12].
"Therefore, brothers, we have an obligation—but it is not to the sinful nature, to live according to it. For if you live according to the sinful nature, you will die; but if by the Spirit you put to death the misdeeds of the body, you will live, because those who are led by the Spirit of God are sons [υἱός (huios)] of God." (Romans 8:12-17)
“You are all sons [υἱός (huios)] of God through faith in Christ Jesus.” (Galatians 3:26)
Here we can see a consensus of the use of “sons of God” within scripture. Yes, these translations utilize "son" - but their source comes from υἱός (huios) in Greek and בֵּן (ben) in Hebrew - both referring to "devoted followers" or "loving servants" in these contexts.

This usage is confirmed by the use of בֵּן (ben) being described as Samuel – as follower or servant in this text spoken by Eli to his student, Samuel (who was not Eli's son):
“My son [בֵּן (ben)],” Eli said, “I did not call; go back and lie down.” (1 Samuel 3:6)
Thus we find the "sons of God" within the above contexts are not referring to physical offspring. Yes, we are all children of God, but this does not explain why some of God's offspring are being referred to as υἱός (huios) or בֵּן (ben) in Hebrew and some are not.

Again, the answer is that υἱός (huios) in this context is, as the Greek lexicon puts it, "one who depends on another or is his follower." In other words, the "son of God" in this context is a loving servant of God, or servant of God. Here are the above-given verses translated with this correction:
When men began to increase in number on the earth and daughters were born to them, the servants of God saw that the daughters of men were beautiful, and they married any of them they chose. (Genesis 6:1-2)
The Nephilim were on the earth in those days — and also afterward — when the servants of God went to the daughters of men and had children by them. (Genesis 6:4)
[Jesus speaking] “Blessed are the peacemakers, for they will be called servants of God.” (Matthew 5:9)
...Adam, the servant of God. (Luke 3:38)
[John, speaking of Jesus] Yet to all who received him, to those who believed in his name, he gave the right to become servants [or representatives] of God. [John 1:12].
"Therefore, brothers, we have an obligation—but it is not to the sinful nature, to live according to it. For if you live according to the sinful nature, you will die; but if by the Spirit you put to death the misdeeds of the body, you will live, because those who are led by the Spirit of God are servants [or representatives] of God." (Romans 8:12-17)
“You are all servants of God through faith in Christ Jesus.” (Galatians 3:26)
Such a translation is consistent with the earliest Christian manuscript found to date, called the Didache, carbon-dated to as early as 50 AD. It is obvious from this text that Jesus, like David, was considered by early Christians as the servant of God. We find the following verse in Didache:
“We thank thee, our Father [LORD], for the holy vine of David Thy servant, which You madest known to us through Jesus Thy Servant; to Thee be the glory for ever.” (Didache, Chapter 9. The Eucharist. Roberts-Donaldson Translation)