"Produced" in Mt 1:2–16
I've recently changed my translation of egennesen (ἐγέννησεν) from "he was the father of" to "he produced" throughout the whole genealogy (verses 2–16). This better fits with the focus in Matthew 1 on how messianic heirs are produced. And specifically how Jesus was (not) produced.
One of the things that is undercut/demoted in the Gospel of Matthew is the prerogative and authority of the earthly father so it makes sense why 'father' does not appear in Matthew chapter 1. In fact the first appearance of the Greek word for 'father' is in relation to the abominable Herod in Mt 2:22.
Mt 1:1 Book of Genesis/Story of Origin
I've made more progress on the meaning of the first two words in Mt 1:1 namely biblos geneseos (βίβλος γενέσεως).
Both biblos and genesis are words with sacred or supernatural undertones and both words could also indicate a 'story', 'narrative', or 'history'.
Genesis was already the title for the sacred book of Genesis in Greek. And biblos was commonly used to signify a holy book/scripture/writing. (Similarly the word for 'writing' [γραφή] used in the Greek New Testament meant 'sacred writing'.)
But things get very interesting when we look at all the meanings of genesis... the Greek word genesis could refer to numerous kinds of 'being' relating to:
source-of-being (origin);In other words the genesis of a person could be about a person's origin/origins (ancestors, the 'cause' of someone's being) or about someone's creating/producing (descendants, the result of someone's procreating). However, it could also be about special events related to birth or someone's whole consequential life, or someone's life purpose (destiny).
manner-of-birth (special associated birth events);
a social 'generation'/age.
Most readings of Matthew have presumed that genesis in Mt 1:1 is not about someone's resulting life (existence) but simply about someone's history (ancestors) because of what follows it is a genealogy (verses 2-16).
But it may be a surprise to know that the Bauer-Danker lexicon/dictionary actually gives the meaning 'life' for Mt 1:1.
I too began to think that 'life of Jesus' was a radical new way of interpreting Mt 1:1 until I checked the Bauer-Danker lexicon! But why then does hardly anyone interpret genesis in Mt 1:1 as 'life' (of Jesus)?
Well the same lexicon (BDAG) also gives another meaning for genesis in Mt 1:1 (ancestral line/lineage) and this second meaning has unfortunately dominated English translations.
Note that the meaning 'life story (of Jesus)' is also due to it's combination with biblos. So the 'story' part mainly belongs to biblos. The 'life' part mainly belongs to genesis (I say mainly because there is some overlap in the functions of both words).
We should compare the beginning of Tobit for it's use of biblos (βίβλος):
Βίβλος λόγων Τωβιτ τοῦ Τωβιηλ τοῦ Ανανιηλ...(Note how 'story' is implied by the word biblos, βίβλος).
This book tells the story of Tobit, son of Tobiel, son of Hananiel...
And if we compare the first verse of Mark:
Ἀρχὴ τοῦ εὐαγγελίου Ἰησοῦ χριστοῦwe can see that both Matthew and Mark concern origins: the origin of the Gospel (Mark), and the origin of Jesus (Matthew). In this regard Matthew actually has something in common with John (origin of the Logos).
Beginning of the Gospel of Jesus Christ
Now the word genesis appears again in Matthew in verse 18 where it answers the question: What caused his life? That is, Jesus' divine origin (conception) is revealed to Joseph who is instructed to accept the child and marry Mary.
But genesis in Mt 1:1 seems less appropriate because it does not initially answer the question What caused his life? And it does not initially answer the question What did he create/produce (descendants, new life, inauguration of the kingdom? - perhaps some of these suggestions would have to take genesis as referring only to the larger gospel narrative?).
Probably genesis should not be translated as ancestors/genealogy or descendants (although in the larger story Jesus' true kin are produced by virtue of the person of Jesus who comes to set in motion the kingdom - but this reading would have to ignore the genealogy...perhaps that is why such a reading has never been considered..?).
What immediately follows Mt 1:1 is an account of what caused Joseph's life (ancestors). What 'produced' Joseph is explicitly not what 'produced' Jesus.
(But perhaps, in the mind of many translators, Joseph's receiving Jesus into his Davidic line legitimates genesis as 'genealogy' in Mt 1:1?)
Craig Keener notes that genesis in verse 1 expects to narrate what Jesus produced (the descendants of Jesus) since this is how it is usually used in Genesis. Keener solves the 'problem' by saying that Matthew is saying that Jesus' ancestors depend on Jesus for their existence (Jesus produced Israel?). This is an interesting line of thinking which Keener does not fully explore.
What commentators like Keener are correct in alerting us to is that the usual categories of 'genesis' might need reconsidering (part of the problem is that the New Testament lexicons only give a small sample of the meanings of genesis - Liddell-Scott has the fuller list).
I suggest that there is (at least) one unexplored option worth considering.
When genesis appears in verse 18 it means 'conception' but not of an ordinary kind. As the BDAG lexicon says here it is "the coming into being at a specific moment" but with special reference "to circumstances under which the birth took place" (namely divine origin/divine shaping of events). So when genesis means 'birth' (as in verse 18) it really means something more than simply 'birth' it means the things and events that Jesus is 'born into' or 'born from' namely divinely so (and anyway there is a more ordinary Greek word for 'birth' namely the similar sounding γέννησις).
So I suggest that the story of the 'life' of Jesus actually includes what foretold Jesus' life. Foretelling/predicting and destiny also belong the meanings of genesis. This aspect has never been explored to my knowledge in Matthew. This seems odd given that in Matthew divine providence and fulfillment is specifically made explicit.
To try to reduce the production/generation down to cause-of-life or consequential-state-of-life has not gotten interpreters and translators very far.
Perhaps the question answered in Matthew 1 is not what is the cause (or state) of Jesus' life but what is the foretelling and destiny of Jesus' life? Biblical Israel was divinely conceived (when Abraham was called out) and it is biblical Israel that provides the foundation of its expected Messiah, according to Matthew.
I'm still figuring this out and still unsure of a good translation. Until then 'story of origin' may have to suffice (but it's a providential origin).