In Matthew 1:16 Jacob is said to be the father of Joseph the husband of Mary. It does not say that Joseph begat Jesus, but only that Joseph was Mary's husband, and Mary gave birth to Jesus.
Luke's records, "And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was the son of Heli" (Luke 3:23) Therefore the verse is indicating that Joseph was Jesus' step son, and that this genealogy is not of Joseph, which clearly if a genealogy of Jesus, would mean this is Mary's linage. Therefore, Jesus was a descendant of Mary, who was a descendant of David and of the Tribe of Judah.
Jesus linage as the descendant of David is established legally through his step father Joseph and physically through Mary His mother.
On comparing the two genealogies, it will be found that Matthew, writing more immediately for Jews, deemed it enough to show that the Saviour was sprung from Abraham and David; whereas Luke, writing more immediately for Gentiles, traces the descent back to Adam, the parent stock of the whole human family, thus showing Him to be the promised Messiah, the "Seed of the woman who would bruise the head of Satan (serpent)." (Gen. 3:15)
Twelve verses in the New Testament state that Jesus was the son of David. (Matt 1:1; 9:27; 20:30; Mark 10:47; 12:35; Luke 6:3; 18:38; Acts 1:16; 7:45; Rom. 1:3; 2 Titus 2:8; Rev. 22:16) In Revelation 22:16, Jesus Himself said, "I Jesus have sent mine angel to testify unto you these things in the churches. I am the root and the offspring of David, and the bright and morning star."
So, a Christian believes the word of God and accepts what it says. Repeatedly Jesus is said to be the descendant of David. Jesus said it Himself....so we accept that as true. Further, we in Occidental society trace linage through the father, oriental people trace it through the mother and father. For example today to "aliyah" to Israel and obtain Israeli citizenship to obtain Israeli citizenship the mother or father must have been an Israeli citizen. In the 1950 "Law of Return" it states a Jew is one who had a Jewish mother. My descendants are Jewish through my father who as an Abrams. But my mother was Irish, and then technically by the Israeli culture I am not a true Jew. I claim linage, but not nationality.
The "law of return" to obtain Israeli establish national citizenship says;
I cannot fully explain the genealogies of David as recorded in 1 Chronicles 3:1f. This has not be a priority so I have not sought to understand it, nor compare it to the New Testament genealogies. I can see that this lists the descendants of David by his various wives and concubines. I have noted that Nathan is listed as David's son in 1 Chronicles and in Luke's linage, but not in Joseph's. In Matthew's account, the line is traced through David's son, Solomon (Matt 1:7). So clearly the linages in Matthew and Luke are two different genealogies one being of Joseph, Jacob's son and the other logically of Mary, Heli's daughter.
God says this about the Bible, "For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost." (2 Peter 1:21) He also said "All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: That the man of God may be perfect, thoroughly furnished unto all good works." (2 Timothy 3:16-17)
So the Bible is not to be compared to extra biblical ancient writings of fallible men, but accepted as God's inspired word. The problem is that often without having the full knowledge of the history and culture of a particular times we subject to make false conclusions. But if we interpret the Bible, we must do so in the analogy of the faith...meaning its clear foundational statements. God's inspired the Bible and therefore it is accurate. So our bias or presupposition is that repeatedly the Bible says Jesus is the descendant of David, so the matter is settled. If we find, what we suppose is a contradiction, then the hermeneutical rule, of interpreting in the analogy of the faith, would preclude that we have a wrong interpretation. Therefore the Bible student must continue his studies till he finds the interpretation that in is in harmony with the rest of what the Bible says.
This, of course, is not a rule of non-biblical hermeneutics. Men are fallible and even eye witness accounts can be different. But God says He superintend the writing of these sixty six books and that means there are without error. God is perfect in all His ways and cannot lie or make a mistake. There are variances found in the various mss, but we know where they are and they are normally only differences in spelling. Some ancient mss are corrupted such as Aleph, A, B, and the Chester Beaty papyrus mss. But we know where they were copied wrong and what the text should read. The KJV of the Bible is the best English translation we have being based on the Major or Western Text. Could it be improved...? Honestly, yes it could, but that does not mean it is not accurate. Not once in over twenty five years of studying the Bible have I seen an error authenticated.
I know that you are honestly seeking to find answers to your questions. I too find there are some things I have not been able to fully understand, but I do not accept them as errors. I admit there is so much I do not know. So, I simply do not make a conclusions, but honestly state my findings admitting I am fallible and do not have all the information on which to make a definitive statement. I am satisfied with this, though I am always seeking to learn more and find the proper interpretation.
Even though some who grasp at straws to try and discredit Luke's statement and the Bible in general, the fact is there was a taxing of the whole Roman Empire under Augustus. This fact is accepted by scholars today, even the most skeptics agree that Luke's statement is a fact.
The verse says, (And this taxing was first (protos) made when Cyrenius was governor of Syria.) (Luke 2:2) The word "first" is the Greek word protos .
Many better Bible scholars would render the words thus, "This registration was previous (protos) to Cyrenius being governor of Syria"--as the word "first" is rendered in Joh 1:15; 15:18. In this case, of course, the difficulty vanishes. p??t?? protos pro'-tos contracted superlative of 4253; foremost (in time, place, order or importance):--before, beginning, best, chief(-est), first (of all), former.
John bare witness of him, and cried, saying, This was he of whom I spake, He that cometh after me is preferred before me: for he was before (protos) me. (John 1:15)
If the world hate you, ye know that it hated me before (protos) it hated you. (John 15:18)
Of course if a person is looking to discredit God's word, they will go to any length. Any honest person who truly studies the Book of Luke, knows he was methodical in the details he gives of the life of Christ and that he was 100% accurate. This has been proven again and again by honest men.
I hope this helps. " Let thy mercies come also unto me, O LORD, even thy salvation, according to thy word. So shall I have wherewith to answer him that reproacheth me: for I trust in thy word." (Psalms 119:41-42)
"Every word of God is pure: he is a shield unto them that put their trust in him." (Proverbs 30:5)
Our trust in God's word is not a blind trust, but based in facts that came be proven. The problem is not with God's word, but with those who will not accept our Creator and Savior.