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Argument 2
Matthew 1:8 omits Ahaziah, Joash, and Amaziah, going directly from Joram to Uzziah. Matthew 1:11 skips Jehoiakim between Josiah and Jeconiah. These passages prove that the word begat skips generations.

Is Argument 2 Relevant?
Here, the Greek word for begat is gennao, which shows flexibility not found in the Hebrew word and does allow for the possibility that a generation or more may be skipped. The only way we would know that a generation has been skipped is by checking the Hebrew passages. However, it is linguistically deceptive to use the Greek word for begat to define the Hebrew word for begat.

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"In any given society, genealogies may function in more than one of the three spheres...it would be possible for a society to have a number of apparently conflicting genealogies, each of which could be considered accurate in terms of its function." [I Studied Inscriptions from Before the Flood, 213] So why are Jesus' genealogies different? Luke's goes all the way back to Adam and has 56 generations. His interest is in establishing a tone of universality in the Gospel message and mission, as he does in Acts with the admission of Gentiles into the Kingdom of God. This is all there is to his purpose, and so the genealogy is linear rather than segmented. Matthew's goes back to Abraham and has 3 groups of 14 generations. But Matthew is trying to prove certain points with his genealogy that Luke is not. He is, first, trying to establish Jesus as a legitimate heir to David's throne, and thus he uses the lineage through known names in 1 and 2 Kings. Second, Matthew has split into blocks of 14 so as to match the Hebrew sum for the numerical equivalent to the name David (14), and to match the breaks with significant events in Jewish history, a "pedagogical device". Finally, Matthew wants to include some women of a questionable character, because they serve as an "in your face" to the expected charge that Jesus' own birth was in some way scandalous or abnormal.

Missing kings? Sure, but again, no problem at all. In the ancient world, genealogies did have gaps, and the reason for this is that this was predominantly an oral culture. In an oral culture, things had to be memorized. Memory was made easiest by making things as short as possible while still retaining their purpose. Such fluidity in genealogical records is not exclusive of the Bible. "By virtue of its form a linear genealogy can have only one function: it can be used to link the person or group using the genealogy with an earlier ancestor or group. The actual number of names in the genealogy and the order of those names play no role in this function, and for this reason names are frequently lost from linear genealogies, and the order of the names will sometimes change." [I Studied Inscriptions from Before the Flood, 213] The removal of names and the telescoping of lists is known in other oral cultures -- and it is also known that certain numerical patterns were preferred. R. R. Wilson [ibid., 196n] notes the example of the Luapula people of Rhodesia, who kept a royal genealogy of nine generations; but the genealogies of common people for the same space were telescoped to between four and seven generations. Elsewhere [Genealogy and History in the Biblical World, 33n] he cites the examples of the Bemba, Tallensi, Tiv, Yoruba, and Cyrenician Bedouin. All of these cultures used telescoped genealogies. And in an oral culture, why not? If Uncle Joe wasn't much to behold, and just sat around in his La-Z-Boy eating chips and burping, why keep him once his kid was secure in the line? Why make us remember more? An oral culture had to make such listings as easy as possible to remember. The royal line required more detail; the common lines less. Another example: West Semitic tribes show a "penchant for a ten-generation pattern" in their genealogies.