The genealogy from Noah to Abraham is thought by many to be complete in Genesis and not at all 'telescoped' like every other genealogy in the Bible. Telescoped basically means that certain people were missed out and only key names were used. Adam can be said to be the father of us all, for instance, or Abraham the father of the Hebrews, leaving out a great many names in between; in both the Old Testament and New, we see the ancient understanding of a genealogy employed consistently.
However, some Young Earth Creationists do not like the fact that Luke includes an extra name in the Noah to Abraham genealogy which we do not find in Genesis 11. This opens up the possibility that the genealogies in the first few chapters of Genesis are incomplete and thus casts doubt on Archbishop Ussher's specific date for the age of earth. They are so quixotic in the defence of their views, they even go so far as to say that the version of Luke which we can prove to be the very best attested and apparently original must be wrong or, worse still, that Luke simply got it wrong! Those who genuinely desire to arrive at God's truth do not close their minds to all reason and hide their beliefs from scrutiny but are rather open and objective. If we believe we already understand all things, how can we learn?
Luke was not wrong but was certainly inspired by the Spirit of God who knows all things.
Cainan is said to be the son of Arphaxad and father of Shelah, yet this is excluded from Genesis:
Genesis 11:12 Arpachshad lived thirty-five years, and became the father of Shelah;
Luke 3:35-36 the son of Shelah, the son of Cainan, the son of Arphaxad (NASB)
However, the Septuagint and Samaritan texts of Genesis 11 include Cainan. The Book of Jubilees and the Sefer ha-Yashar both describe Cainan as a historical figure. In fact, as Smith notes, 'there are more traditions preserved of him than of his son Salah.'
It has even been suggested by scholarly examination of the timing of the writing of the Masoretic Text that Cainan was deliberately not included by the Jews for sociopolitical reasons - see article.
So is there any evidence against Luke's inspiration? The NET Bible notes recognise that whilst two key manuscripts do not include Cainan, the witnesses for his inclusion are substantial. They conclude that 'the omission may be a motivated reading'. And certainly it was not just the Jews who were motivated for removing Cainan from Genesis 11, nor early Christians, such as Irenaeus or Eusebius, trying to avoid the claim of contradictions or errors in the Bible. Even today, there are some who misrepresent Young Earth Creationists, who are motivated by a desire to allow no scholarly foot in the door of their interpretation.
Genealogies which are recorded in one book of the Bible but which deliberately exclude names found in the same genealogy from another book of the Bible are not treated with contempt. They are not criticised away by those with obvious motivation. It is my sincere prayer that the body of Christ would cease wrestling with the above texts also and allow the Bible to shape their interpretation rather than re-shaping the Bible to fit their presuppositions.
May the God of all truth help us!
Titus 3:9 But avoid foolish controversies and genealogies and strife and disputes about the Law, for they are unprofitable and worthless. (NASB)