The difference between Matthew and Luke’s genealogies 

I found it! Finally, I have an answer that explains why the Gospels of Matthew and Luke have different genealogies for Jesus. Please join me today to hear from Agustin on why the Bible does not contradict itself.

Topics: Saints, Scripture, apologetic, family history, Adam, Abraham, proofs for the Christianity, why I speak too fast

(Link to full work: Sermons on Selected Lessons of the New Testament 1-10 | EWTN )

(St. Augustine of Hippo. Sermons on Selected Lessons of the New Testament, 29, 30.)
Added to this; there is another way peculiar to the Jews, in which a man might be the son of another of whom he was not born according to the flesh. For kinsmen used to marry the wives of their next of kin, who died without children, to raise up seed to him that was deceased. (6) So then he who was thus born was both his son of whom he was born, and his in whose line of succession he was born. All this has been said, lest any one, thinking it impossible for two fathers to be mentioned properly for one man, should imagine that either of the Evangelists who have narrated the generations of the Lord are to be, by an impious calumny, charged so to say with a lie; especially when we may see that we are warned against this by their very words. For Matthew, who is understood to make mention of that father of whom Joseph was born, enumerates the generations thus: "This one begat the other," so as to come to what he says at the end, "Jacob begat Joseph." But Luke--because he cannot properly be said to be begotten who is made a child either by adoption, or who is born in the succession of the deceased, of her who was his wife--did not say, "Heli begat Joseph," or "Joseph whom Hell begat," but "Who was the son of Heli," whether by adoption, or as being born of the next of kin in the succession of one deceased.(7)

30. Enough has now been said to show that the question, why the generations are reckoned through Joseph and not through Mary, ought not to perplex us

(Deuteronomy 25: 5-6)
When brothers live together and one of them dies without a son, the widow of the deceased shall not marry anyone outside the family; but her husband’s brother shall come to her, marrying her and performing the duty of a brother-in-law. The firstborn son she bears shall continue the name of the deceased brother, that his name may not be blotted out from Israel.

(Genesis/38: 8-10)
Then Judah said to Onan, “Have intercourse with your brother’s wife, in fulfillment of your duty as brother-in-law, and thus preserve your brother’s line.” Onan, however, knew that the offspring would not be his; so whenever he had intercourse with his brother’s wife, he wasted his seed on the ground, to avoid giving offspring to his brother. What he did greatly offended the LORD, and the LORD took his life too.