This is actually a 15th century innovation by Annius of Viterbo.
Luke 2:23,38: When He began His ministry, Jesus Himself was about thirty years of age, being, as was supposed, the son of Joseph, the son of Eli, the son of Matthat, the son of Levi, the son of Melchi, the son of Jannai, the son of Joseph...the son of Enosh, the son of Seth, the son of Adam, the son of God.
Matthews' genealogy (Mat 1:1-3,16)says (in the opposite order): The record of the genealogy of Jesus the Messiah, the son of David, the son of Abraham: Abraham was the father of Isaac, Isaac the father of Jacob, and Jacob the father of [a]Judah and his brothers...Jacob was the father of Joseph the husband of Mary, by whom Jesus was born.
I don't see the genealogy of Mary here. No one in the Middle East in those days counted genealogies accoridng to female lines. Inheritance (birthright) was strictly along male lines. Women were "fertile ground" and men were carriers of family "seed." All genealogy belong to male "seed" in ancient Israel. Thus, S. Jerome, who was very familiar with Jewish customs and language says "It is not the custom of the scriptures to count women in their genealogies."
The two accounts give different starting points and different fathers of +Joseph, namely Eli and Jacob. Luke's account traces the lineage all the way back to Adam, the Son of God (my emphasis). Matthew's genealogy begins with Abraham.
The numbers and names of generations don't match either. The divergence, aside form Joseph's father begins in ancestor number 5 (Elezear/Levi according to Matthew/Luke respectively).
Where is there a disagreement?
Minor details such as who heard/saw what. Also Acts says +Paul wen to Jerusalem twice and +Paul says it was once. Acts never repeat what +Paul claims in Gal 4:14, as having been received "as an Angel of God, as [wV] Christ Jesus." Talk about "alter Christus" and the Chirst-complex!
There are many other differences also, too numerous to list.
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