According to Thayer's Lexicon, the Greek word 'gennaō', rendered 'begotten' in our English translations simply refers to fathers begetting or fathering children. In a metaphorical sense, this could be understood as the apostle Paul's 'adoption' of Timothy ( I Corinthians 4:17 ) ! However the context determines the specific meaning of the word, it is used most often as the fathering, or producing of a child, or protoge', if you will. In the passage above, the Greek 'anagennaō' simply means 'to produce again, beget again, beget anew'. The phrase 'only begotten', transliterated from the Greek 'monogenēs' refers to a 'single of its kind, only'. The author of Hebrews uses this same Greek word to refer to Isaac, son of Abraham as John uses to describe Jesus in several different passages ( John 1:14, 18, 3:16, 18 ), including in His Letters ( I John 4:9 )!
In Genesis 22, where it is recorded that the God of Heaven & Earth told Abraham, 'Take now your son, your only son Isaac, whom you love, and go to the land of Moriah, and offer him there as a burnt offering on one of the mountains of which I shall tell you', the Author used the Hebrew 'yachiyd', meaning 'only, especially only begotten, only child'! Again, depending on the context, this may have a literal meaning, as in Judges 11:34 where Jepthah truly only had one daughter, tor a metaphorical meaning as the passage above where it refers to the fact that Abraham had only one son by promise, whereas Ishmael had been born according to the will of the flesh. All this is to say that the context determines the conveyed meaning; though we ( corporately, as the Body of Christ ) are never referred to as 'the only begotten' of The Father, we are 'begotten' of the Father, especially in a spiritual or metaphorical sense, by the Resurrection from the Dead!
The key, one might say, to differentiating between the Body of Christ & the Creator ( Father ) Himself is that little but oh, so important word 'only'! Jesus, traditionally called 'the God-Man', was in essence the Creator Himself. There are numerous instances in the Greek Scripture where Jesus angered the Pharisees by claiming that He was One with the Father! John in fact says that without Him 'nothing was made that was made' ( John 1:3 ). Being of one Essence with the Father, as the creeds rightly say, Jesus was sent from the Father's Side ( much as Eve was from Adam's ) to put things to rights & to institute the Marriage of Heaven & Earth, in effect, to make the Dwelling of God with Man, once again, as in the Beginning!
Promised by the Creator of Heaven & Earth, as was Isaac before, Jesus was sacrificed on a mountain ( hill, really )! He was, as Isaac was, the 'only' Son of the Father. In the greatest sense, we too, as the Body of Christ, might be called the 'only begotten' of the Father, for we too are the Promised Seed! Jesus WAS the Promised One, but as His Body, metaphorically speaking, we were promised as well; David wrote of 'a people yet to be created' ( Psalm 102:18 ). Through the prophet Isaiah, the Living God spoke these words of this people, 'You shall be called by a new name'! This New Name was not Jesus, or even Christian, though we ARE called that; this New Name was a metaphor for our True Identity, the Son of the Creator God, our Heavenly Father!
Charles Haddon Shank