“Μονογενη (monogene)” is a compound word of “mono” (only) and “gene” (begotten). The literal translation is “only begotten.” This definition fits the context. Jesus is not simply God’s “one and only” son. Adam is God’s son (Luke 3:38). God has many angelic sons (Genesis 6:2). But whereas these other sons were “created” sons, Jesus is God’s only "begotten" son. This distinction, ripe with theological significance, is made clear only by translating μονογενη as “only begotten.” Scholars who argue that μονογενη just means "unique" are semantically pulling the cart ahead of the horse. Jesus is "unique" because he is God's only begotten son.
Modern lexicologists who believe that μονογενη merely means “one and only” apparently only consider the way in which Greek writers used the word in reference to the only child of a human parent. Since human parents cannot “create” a child in the sense that God did with Adam or the angels, an “only begotten” child of a human parent would always be the “one and only” child. However, this is not the case with God; so we should not define μονογενη as “one and only” when it is used in reference to the only begotten son of God, Jesus Christ. What may be redundant and obvious in regards to a human son (that he was begotten) is not redundant in regards to the eternally begotten Son of God.
D. A. Carson refers to the usage in the LXX to make a point against translating μονογενη as "only begotten" (Exegetical Fallacies, pp. 30-31). He says the LXX uses μονογενη to translate the Hebrew "יחיד (yahid)" at Psalm 22:20 and 25:16 - passages which he says are "without even a hint of 'begetting'". Carson is semantically pulling the cart ahead of the horse. Psalm 22:20 says, "Deliver my soul from the sword; my darling from the power of the dog." The "darling" is the Hebrew "יחיד (yahid)", meaning "only", translated as μονογενη in the LXX. By "darling", the speaker's precious life is signified. But how do we get from a word that means "only" to the intended meaning of "precious life"? We must remember that the Psalms are poetry. The intended meaning is accomplished through the speaker metaphorically referring to his precious life as his only begotten child. In Hebrew thought, the most precious thing in life was one's only begotten child (as it was for Abraham and also our Father God). It is by first establishing this metaphor of that which is culturally considered the most precious that we get to the signified meaning of "precious life". "יחיד (yahid)" by no means signifies "precious life" apart from the metaphor of an only begotten child. As for Psalm 25:16, it appears the LXX translators interpreted the speaker as being an only begotten child with no other siblings - hence being alone in the world. In any event, the LXX is just a loose translation so its choice of words cannot be assumed to carry the meaning of the literal Hebrew.
Critics argue that μονογενη should be translated “one and only” since the word is used in Hebrews 11:17 to describe Isaac, who supposedly was not the “only begotten” son of Abraham (Abraham also begat Ishmael). To make sense of why “only begotten” is used in Hebrews 11:17 to refer to Isaac (even though Ishmael was also begotten by Abraham) we must understand that Hebrews 11:17 makes a point about possession rather than genealogy. Abraham’s faith is commended in Hebrews 11:17 because he offered up to God the only son whom he possessed at the time - Isaac. In Genesis 22:2, God refers to Isaac as Abraham’s “only begotten son” because from Genesis 21 onward Ishmael was no longer under Abraham’s custody. Since Abraham no longer had custody over Ishmael, Isaac was indeed his “only begotten son.”
Read more articles from: The King James Version is Demonstrably Inerrant