Some here have fallen into a word study fallacy. The only true way to find out the meaning of a word is to study the use of the word synchronically. I’ve mentioned previously that the word “nice”, if one does a word study as is often done on the BB, means “stupid”. The history of a word and it’s etymology do not determine a word’s meaning or use within a specific context.
With μονογενης there are two main interpretations – it means “unique”, “one of a kind”, or it means “only begotten”.
Part of the issue, and disagreement, involves its etymology. If this compound word (μονογ and ενης) is derived from monos (only) and genos (kind) then it means “unique”. If this word is derived from monos (only) and gennao (begat) then it means “only begotten”.
Unfortunately there is no consensus among scholars, and we cannot really know as a fact how the word originated.
Etymology
In support of the word meaning “only begotten”, the ending ενης commonly is used in compound words to indicate “begotten”. Some examples include αγεηνς (unnoble birth), δυσγενης (low born), ευγενης (well born), παλιγενης (born again), and πρωτογενης (first born).
So we know, without a doubt, that the ending ενης often means “begotten” (I am unaware of ενης being used to mean “kind” or “type”, but allow for that possibility.
Usage
The etymology of a word is only the first step in determining a word’s meaning. We also need to look at how the word is used, and the context in which this word is used.
Luke 7:12-13 - Now when he came nigh to the gate of the city, behold, there was a dead man carried out, the only (μονογενης) son of his mother, and she was a widow . . .
In this context, μονογενης means “only begotten” (the dead man was the only begotten son of his mother….not the unique son of his mother).
Luke 8:41-42 - And, behold, there came a man named Jairus, and he was a ruler of the synagogue: and he fell down at Jesus’ feet, and besought him that he would come into his house: for he had one only (μονογενης) daughter, about twelve years of age, and she lay a dying.
Again, here Jairus comes on behalf of his only begotten daughter (he only has one daughter, not a one of a kind daughter but he had begat only one daughter).
This is the same in John 1:14 - And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten (μονογενης) of the Father,) full of grace and truth.
Here Jesus is the only begotten of the Father (not the only unique of the Father, or the only one of a kind of the Father).
Anhanasius uses the word to mean "begotten" in contrast to adopted (a narutal born child).
Josephus uses the word to mean "begotten" in his historical secular genelogy.
Hesiod, in Theogony, uses the word to mean "only begotten".
Aesop uses the word to mean "only begotten child".
Aeschylus uses the word to mean "only begotten".
Scholarship
Charles Irons (Fuller Theological Seminary) argues that the word means “only begotten”. He notes that Plato (Critias) uses the Greek word to mean “only begotten”.
Bulman insistes that the word means “only begotten” because of the context. The context is generation. If the word means “unique” or “one of a kind” then it is an empty modifier and one must add to Scripture (“son” is implied in “begotten” but not in “unique”). He also notes that ενης refers to “generation” in other Greek words.
Thayer argues that the word refers to a descendent or child (regardless of gender), and therefore the appropriate interpretation is “only begotten”.
Büchsel interpreted the word to mean "only begotten" in the context "of sole descendent".
Dahms observes that when used in reference to persons the word always points to generation (begotten).
Bottom Line
The bottom line is that we cannot dismiss “only begotten” simply because we do not like it. It is a legitimate interpretation of the word. People cannot disprove this fact. They cannot prove an opposing position.
They can argue for an opposing position. They should argue an opposing position. But anything more is dishonest.