Cainan

Why do some question the authenticity of the phrase, “Shelah, who was of Cainan, who was of Arphaxad” (Luke 3:35-36)?
The “Cainan” in this phrase is not mentioned in the Old Testament, which states, “Arphaxad begot Shelah” (Genesis 10:24 and 1 Chronicles 1:18) and even specifies that “Arphaxad lived thirty-five years and begot Shelah” (Genesis 11:12). Since the Gospel of Luke mentions another “Cainan” in the very next verse - “Mahalalel, who was of Cainan, who was of Enosh” (Luke 3:37-38), the speculation is that an ancient copyist making a handwritten copy - a "manuscript" - of the Bible must have made a mistake and written “Cainan” twice instead of just once.

Is that true?
No, for two reasons. Firstly, while the proximity of the two men named “Cainan” in Luke 3:36-37 makes it possible for one of them to be an erroneous duplication, their proximity also makes it all but certain that such an error would have been detected and caught by those who read it or by the copyist himself, saying, “Wait a second, I just read/wrote that Cainan was (the son) of Arphaxad; Cainan is now (the son) of Enosh?” It should be noted that “Cainan” is a very rare name in the Bible. Had one of the two been a copyist error, there would be only one man named Cainan in the entire Bible. Such a unique man being said to have two different fathers in consecutive verses would not have gone unnoticed. Secondly, if such a copyist error somehow had gone unnoticed and continued to be copied, it would be found in only some of the manuscripts of Luke that have been discovered to date. In reality, both the “Cainan who was of Arphaxad” and the “Cainan who was of of Enosh” are found in almost all manuscripts of Luke discovered to date. (The only two exceptions are Papyrus Bodmer XIV, a poor copy of Luke 3:18-24:53 that is also missing hundreds of other words, including all or parts of Luke 11:4, 16:19, 22:43-44, 23:34; and Codex Bezae Cantabrigiensis, which is also missing many words, including the entirety of Luke 11:32 & 36, 12:21, 19:25 & 33, and 24:12.)

If Arphaxad is Shelah's grandfather, not his father, why do Genesis 10:24 and 1 Chronicles 1:18 both say “Arphaxad begot Shelah”?
The root of יָלַ֣ד (yalad), the original Hebrew word translated “begot,” means “to bear” or “to bring forth” one's own child or a later descendant. For example, Genesis 46:15-18 names Leah's sons, grandsons and two great-grandsons (Hezron and Hamul), and then declares that she “bore” - יָֽלְדָ֤ה (yaledah) - all of them. It should also be noted that in the Jewish context, “son” can refer to any male descendant, and “father" can refer to any male ancestor. For example, Matthew 1:1 introduces Jesus as the “Son of Abraham,” whom the Pharisees call their “father” (John 8:39).

But Genesis 11:12 says “Arphaxad lived thirty-five years and begot Shelah,” so how can he be a grandfather at 35 years of age?
The average age of fatherhood, in the late 20s today, was much younger back then. Girls were married off soon after they became able to bear a child, and boys married soon after they became able to support a family; both typically married as teenagers. Arphaxad and Cainan could have become fathers at 18 and 17 years of age, respectively, or vice versa.

Why don't the Samaritan Pentateuch, the Aramaic Targum, and the early versions of the Greek Septuagint mention Cainan the son of Arphaxad, as some complain about today?
They are all translations of the Hebrew Old Testament. Since the original Hebrew Old Testament doesn't mention him, neither will its translations.

Are there any ancient Hebrew sources that mention him?
He is mentioned by Demetrius, a Jewish historian who lived in the third century BC, while another Jewish document, fragments of which were found among the Dead Sea Scrolls, names Cainan the son of Arphaxad, as well as Cainan's wife and his great sins.

Why does the New Testament mention someone from the Old Testament era that the Old Testament doesn't mention?
Two of those who resisted Moses in the Old Testament are identified as “Jannes and Jambres” only in 1 Timothy 3:8 of the New Testament, so Cainan the son of Arphaxad isn't the only Old Testament figure who is identified only in the New Testament. Both the Old and New Testaments were inspired by God, who used human instruments to tell us no more and no less than what He wants to tell us, when He wants to tell us.