A problem with the record of genealogy of the Messiah

First, let us have a look at Matthew 1: 

This is the genealogy of Jesus the Messiah the son of David, the son of Abraham:

2 Abraham was the father of Isaac,

Isaac the father of Jacob,

Jacob the father of Judah and his brothers,

3 Judah the father of Perez and Zerah, whose mother was Tamar,

Perez the father of Hezron,

Hezron the father of Ram,

4 Ram the father of Amminadab,

Amminadab the father of Nahshon,

Nahshon the father of Salmon,

5 Salmon the father of Boaz, whose mother was Rahab,

Boaz the father of Obed, whose mother was Ruth,

Obed the father of Jesse,

6 and Jesse the father of King David.

David was the father of Solomon, whose mother had been Uriah’s wife,

7 Solomon the father of Rehoboam,

Rehoboam the father of Abijah,

Abijah the father of Asa,

8 Asa the father of Jehoshaphat,

Jehoshaphat the father of Jehoram,

Jehoram the father of Uzziah,

9 Uzziah the father of Jotham,

Jotham the father of Ahaz,

Ahaz the father of Hezekiah,

10 Hezekiah the father of Manasseh,

Manasseh the father of Amon,

Amon the father of Josiah,

11 and Josiah the father of Jeconiah and his brothers at the time of the exile to Babylon.

12 After the exile to Babylon:

Jeconiah was the father of Shealtiel,

Shealtiel the father of Zerubbabel,

13 Zerubbabel the father of Abihud,

Abihud the father of Eliakim,

Eliakim the father of Azor,

14 Azor the father of Zadok,

Zadok the father of Akim,

Akim the father of Elihud,

15 Elihud the father of Eleazar,

Eleazar the father of Matthan,

Matthan the father of Jacob,

16 and Jacob the father of Joseph, the husband of Mary, and Mary was the mother of Jesus who is called the Messiah.

17 Thus there were fourteen generations in all from Abraham to David, fourteen from David to the exile to Babylon, and fourteen from the exile to the Messiah.

St.Luke goes further and relates Jesus to Adam, The Son of God. 

Interestingly, in both gospels, Jesus is connected to David through Joseph. However, before Joseph and Mary were married, Mary was pregnant "through the Holy Spirit". Matthew makes it clear that "he had no union with her until she gave birth to a son." So Joseph, according to the gospels, is not Jesus' father. Jesus, since he had no earthly father, cannot be a direct male descendant of David, and therefore cannot be the Messiah. Is this a valid objection?

In response, it is claimed that Joseph adopted Jesus, and passed on his genealogy via adoption. There are two problems with this claim:

a) There is no Biblical basis for the idea of a father passing on his tribal line by adoption. A priest who adopts a son from another tribe cannot make him a priest by adoption;

b) Joseph could never pass on by adoption that which he doesn't have. Because Joseph descended from Jeconiah he fell under the curse of that king that none of his descendants could ever sit as king upon the throne of David. (Jeremiah) 

To answer this difficult problem, apologists claim that Jesus traces himself back to King David through his mother Mary. However: 

a) There is no evidence that Mary descends from David. Both Matthew and Luke show Jesus' claim through Joseph. If Mary had a claim, then surely they would have used her genealogy, as this was more likely to be accepted as authentic. 

b) Some scholars have argued that Jesus cannot be related to David through Mary because even if Mary can trace herself back to David, that doesn't help Jesus, since tribal affiliation goes only through the father, not mother. (Numbers 1:18)  

c) Even if family line could go through the mother, Mary was not from a legitimate Messianic family. According to the Bible, the Messiah must be a descendant of David through his son Solomon (II Samuel 7:14)  The third chapter of Luke is irrelevant to this discussion because it describes lineage of David's son Nathan, not Solomon. (Luke 3:31) 

d) Luke 3;27 lists Shealtiel and Zerubbabel in his genealogy. These two also appear in Matthew 1:12 as descendants of the cursed Jeconiah. If Mary descends from them, it would also disqualify her from being a Messianic progenitor.

If we have a look at Luke's genealogy, he begins by saying, "He was the son, so it was thought, of Joseph."

 Some scholars have pointed out that Luke was suggesting Jesus was actually the son [i.e. descendant] of Eli. Since Jesus' actual physical descent was through Mary, his closest male ancestor (Eli) would be Mary's father. The word "son" in Hebrew can be used of multi-generational descent, as in the English word "descendant."This makes Luke's genealogy a record of Mary's ancestry.That Eli was Mary’s father may also be confirmed by the rabbis in the Jerusalem Talmud, which mentions a Mary the daughter of Eli/

So, in that case, we can fall back on Luke's genealogy of the Messiah. Although Jesus hasn't descended through His father, Genesis' requirement of the Messiah is only that he will be of the tribe of Judah.  Isaiah says only that he will be a descendant of Jesse (the father of King David). Jeremiah says only that he will be a descendant of David himself. So there is no reason why the Messiah cannot be descended from David on his mother's side.

The objection that tribal affiliation is only through the father is not always true. If a man has only daughters, the tribal inheritance is through the daughters (Numbers 27;7). This might well have been the case with Mary, since only her sister is mentioned in John 19 and not a brother. But even so, since Mary was still living at home and Joseph was not the father of her child, there would be no one else to trace the child’s heritage through other than Mary and her father. This is exactly the implication of Luke: that Jesus was a descendant of Eli.

So there is no serious objection to accepting Luke’s genealogy as the actual physical genealogy of Jesus through his grandfather Eli and his mother, Mary. He was a physical descendant of King David, and therefore eligible to fulfill the prophecies pointing to the Messiah.

So you might wonder then, what is the purpose of Matthew's genealogy? 

Jesus was born into the betrothed relationship of Joseph and Mary, which was legally a family unit ( among the Jewish people, betrothal was a legal marriage, though not yet consummated). If accepted by the husband, the child became legally part of the family, which Joseph did when he “took” Mary as his wife. That he “took” her means that they proceeded to the second stage of marriage where they began living together. In this way, Jesus could also legally restore the royal line from Solomon through Jeconiah without being a physical descendant of Jeconiah and running afoul of Jeremiah’s prophecy. In other words, a miraculous birth was exactly what was needed both to fulfill prophecy and to reestablish the royal line of David. As Amos prophesied: “In that day, I will raise up the booth of David which is fallen and I will close up their breaches and his ruins I will raise up; and I will build it as in the days of old” (Amos (9:11). One final point. It is noteworthy that neither the Pharisees nor Sadducees, bitter enemies of Christianity, never challenged these genealogies. The lists made by both Matthew and Luke were comprised of names publicly recognised by the Jews at that time as authentic.