For to which of the angels did He ever say, "You are my Son..."? (Hebrews 1:5)
...as many as received Him, to them He gave the right to become children of God, even to those who believe in His name...(John 1:12)
Whenever we discuss the name "the Son of God," and perhaps especially in "Western" and/or postmodern culture(s), there is a subtle danger of generalizing the term in such a way that we fail to comprehend its uniqueness and singularity. If this is the case then, crucially, we will fail to understand who Jesus, the Son of God, really is (even in the limited capacity to which we can, by His grace and mercy, comprehend Him). Furthermore, we may mistakenly import our ideas about this concept by disregarding the original intent. As a result, we are left with a concept of filiality (that which pertains to daughters and sons) that is so broadly construed it can no longer capture the purposefully distinguishing nature of the term. Yet, God's desire is such that we know Him, for "we know that the Son of God has come, and has given us understanding so that we may know Him who is true" (1 John 5:20).
One way in which we commonly generalize the name "Son of God" is through the seemingly innocent claim "we're all God's children." Depending on what one means by this claim, we can inadvertently (attempt to) diminish the uniqueness of filiality as it applies directly to Christ as well as to humanity through Christ. If for example, by this phrase we mean that by virtue of being human, or by virtue of being created, we are "all God's children," then this mentality discords with a biblical conceptualization of filiality.
The problem with such a concept is that it operates on the assumption that filiality as it relates to God is universally automatic and inherent, and this does not resonate with the teaching of Scripture. Under the biblical framework, filiality entails a privileged relationship that is either possessed innately or entered into. Moreover, each of these aspects relates intimately to the Person and work of Jesus Christ.
Essentially, Jesus is the sole Person to whom sonship inheres, since He is eternally, and by necessity of His unchanging nature, the Son. God reveals to us the eternal, and thus inherent, nature of His Son throughout much of St. John's writings:
In the beginning was the Word, and the Word was with God, and the Word was God...And the Word became flesh, and dwelt among us, and we saw His glory, glory as of the only begotten from the Father, full of grace and truth (John 1:1, 14)
By this the love of God was manifest in us, that God has sent His only begotten Son into the world that we might live through Him (1 John 4:9)
Moreover, we find that God directly and emphatically declares Christ's nature as Son, both at His baptism and on the Mount of Transfiguration:
being baptized, Jesus came up immediately from the water; and behold, the heavens were opened and he saw the Spirit of God descending as a dove and lighting on Him, and behold, a voice out of the heavens said, 'This is My beloved Son, in whom I am well-pleased' (Matthew 3:16-17)
Jesus took Peter and James and John his brother, and led them up to a high mountain by themselves. And He was transfigured before them; and His face shone like the sun, and His garments became white as light...a bright cloud overshadowed them, and behold, a voice came out of the cloud and said, 'This is My beloved Son, with whom I am well-pleased; listen to Him!' (Matthew 17:1-2, 5)
So, we see that Jesus alone is definitively the Son of God, and this name derives from His eternal nature in which He exists and has existed from the beginning. By claiming that "we are all God's children," we actually diminish Christ's nature (from the point of our perception) by falsely attributing inherent filiality to ourselves.
However, being a son or daughter of God is available to humanity, and it is available universally. God, having created us to experience intimate fellowship with Him and with His Son (see 1 John 1:3), enables us to become His daughters and His sons. We enter into this privilege; being "created" by God does not necessarily entail a filial relationship, though it does implicate a Creator-created relationship that inheres to us. Our filiality receives substance because of Christ's eternal nature as Son, and our subsequent being found in Him; our ability to enter into this unique relationship derives from Christ's Person and His work of offering Himself to God wherein "we become the righteousness of God in Him" (2 Corinthians 5:21). Again, claiming that "we are all God's children" assumes that this relationship is automatic, and ignores the fact that our being daughters and sons of God is a privilege that we enter into and derives entirely from Jesus.
If we can but stop to contemplate this magnificent truth, we can see how beautiful and humble is the manner in which a holy and infinite God condescends to our state in order to pursue a relationship with us. And, even more incredible, this is a relationship that we in no way deserve to possess. This latter point becomes readily apparent when we consider how we really treat Jesus, the True Son - before ascending into heaven He suffered and died on our behalf, taking the punishment of our sins, and He did this so that we might be called not only friends (see John 15:15), but brethren (see Hebrews 2:11), and children:
See how great a love the Father has bestowed on us, that we would be called children of God; and such we are (1 John 3:1)
God's love is so great toward us that He gave His only begotten Son so that we might become His daughters and sons, entering into a unique and special relationship with Him, and there is nothing higher or greater than can offer more satisfaction.
Though the ability to acquire filiality is universal - God offers this to all of humanity without partiality - it's application depends on our response. Though God wholly desires to give us the highest good, Himself, He knows that real love does not impose forcefully; instead God constantly pursues us - always extending His hand toward humanity - but in His sovereign wisdom He allows us the choice to believe, and,
as many as received Him, to them He gave the right to become children of God, even to those who believe in His name (John 1:12)
His hand is extended still.
God has given us eternal life, and this life is in His Son. He who has the Son has life; he who does not have the Son of God does not have life...And we know that the Son of God has come, and has given us understanding that we may know Him who is true; and we are in Him who is true, in His Son Jesus Christ. This is the true God and eternal life (1 John 5:11-12, 20, emphasis added).