Father Son what do these terms imply?

Question

I'm not so much interested to who or what these words refer to in these verses, but what I would like to know, however, is what the terms 'father' and 'son' mean when used in the Tenach when it’s not really a question of blood relationship within a family but is used proverbially; or as an idiom. Obviously these words express a special bond: but what does it mean when someone calls another who is not his son ‘son’, or who is not his father ‘father’?

Psalm 2:7

Let me tell of the decree: Hashem said to me,[Compare 2 Sam. 7.14, and Ps. 89.27 ff.]“You are My son, I have fathered [begotten] you this day.

Exodus 4:22

Thus says Hashem: Israel is My first-born son.

Deuteronomy 32:6

Is not He the Father who created you, fashioned you and made you endure.

2 Samuel 7:14

I will be a Father to him, and he shall be a son to Me.

Psalm 89:27

He shall say to Me,‘You are my Father, my G-d.’ [And] I will appoint him first-born, highest of the kings of the earth.

Answer 1

Hashem is our Father in Heaven and therefore, whilst He may not be our biological father He created all of us.¹

All your examples are referencing this father-like relationship. We are G-d's chosen people and He functions as "Avinu Malkeinu", both our father and King.

One source that brings out the Father-Son relationship we enjoy with Hashem is Radak on his commentary on Tehillim 2:7 that you reference as your first example.

He writes there:

The Lord said unto me, Thou art My son: – and the kingdom has come to me from Him, and therefore let no man stir up strife against it, for the Lord hath chosen me for a son, as He said to Samuel (1 Sam. 16:1): "For I have provided among his sons a king for Myself." It is as though to say, "This king is Mine and he is My son and servant and obeys Me" - for everyone who is obedient in the service of God He calls His son, just as a son obeys his father and is ready for his service. And so (in the verse) "ye are sons of the Lord your God" (Deut. 14:1), and "I will be his Father and he shall be My son" (2 Sam. 7:14); and it says (Hos. 2:1), "the sons of the living G-d." (Sefaria translation)

This idea can be brought out more when looking at the verse you bring from Devarim 32:6. There in Parshas Ha'azinu, Moshe outlines the Jewish peoples' relationship to G-d and how Hashem is just and fair. Sforno there makes it clear how Hashem is to be viewed like our father:

הלא הוא אביך קנך, He is not like a natural father who had no control over the type of son he had sired, but had to leave this to chance; G-d deliberately adopted the Jewish people giving them the kind of existence that would make Him proud to be called your “owner,” and made Him look forward to achieve His aim in creating mankind through you. Had He not made you into a nation you would have remained an insignificant tribe of sorts. (Sefaria translation)

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¹ Parenthetically, refer to Kiddushin 30b where the Gemara writes:

ת"ר שלשה שותפין הן באדם הקב"ה ואביו ואמו

Our Rabbis taught that there are three partners in (the creation of) man - Hashem and his father and his mother.

Rashi comments there that whilst both the father and mother contribute physical elements to the birth of a child, it is Hashem who breathes in the soul and provides the sight, hearing and speech.

Answer 2

Every relationship between human beings is a way for us to understand part of our relationship with G-d. We can't see him or sense him or really know what it means for G-d to be our king, but we know about human kings and that helps us appreciate what he does for us in that aspect. We can't really grasp what it would mean for G-d to be a husband and Israel his wife, so to speak, but Shir Hashirim (Song of Songs) brings that concept to us, by using the analogy of a woman and her beloved. So too for master and slave, judge and defendant, rich man and beggar, and even neighbor (שכן) - that G-d desires, so to speak [I'm going to run out of כביולs], to dwell among us (his שכינה).
So too for every relationship between human beings. Father and child is one of those and we see in it one of the many ways that G-d deals with us and cares for us.
[I heard this idea from R' Chaim Mintz shlit"a.]