Why do Matthew and Luke give Jesus different family trees, through different sons of David and with different fathers for Joseph?

The two lists are doing different jobs, and neither writer hides it. Matthew runs forward with ‘begat’ through Solomon and the kings of Judah, shaped into three sets of fourteen (Matthew 1:17), to show Jesus as heir of David’s throne through Joseph, who named him and took him as his own (Matthew 1:21–25). Luke runs backward to Adam without ever saying ‘begat’, and begins with Jesus “being (as was supposed) the son of Joseph” (Luke 3:23); in Hebrew usage ‘son’ could mean grandson, son-in-law, legal heir or adopted son, so ‘son of Heli’ need not mean that Heli fathered Joseph.

The explanation most often given today is that Luke traces Mary’s line: Heli was Mary’s father, and Joseph is listed as his ‘son’ by marriage, since family lines were recorded under men’s names. In Luke’s Greek, Joseph is the only ancestor in the list whose name lacks the article tou, ‘of the’, which suits reading ‘as was supposed, of Joseph’ as an aside; and Luke tells the birth from Mary’s side, with Gabriel promising her son “the throne of his father David” (Luke 1:32) though no human father is involved. On this view Jesus is David’s heir by law through Joseph and David’s descendant by blood through Mary. The oldest recorded explanation, from Julius Africanus early in the third century, makes both lists Joseph’s by way of a levirate marriage (see below), and Christians have held both views ever since.

Levirate marriage (Africanus)

Julius Africanus, quoted by Eusebius (Church History 1.7), said he had the account from the relatives of Jesus. Matthan, of Solomon’s line, married a woman named Estha and fathered Jacob; after Matthan died, Melchi, of Nathan’s line, married her and fathered Heli. When Heli died childless, his half-brother Jacob married the widow to raise up a son in his brother’s name (Deuteronomy 25:5–6). Joseph was then Jacob’s son by birth, as Matthew says, and Heli’s son by law, as Luke says. Africanus’s copy of Luke apparently made Heli the son of Melchi; in our text Matthat stands between them, so the same account now runs through Matthan and Matthat.

Royal title and natural descent

Others also take both lists as Joseph’s but explain them differently: Matthew records the line of royal succession, the heirs to David’s throne, while Luke records Joseph’s actual ancestry. If Jacob had no son, the right to the throne passed to his nearest kinsman, and Joseph, the son of Heli, became Jacob’s heir.

Matthew’s fourteens

Matthew’s list is a structured summary, arranged in three sets of fourteen and leaving out several kings (see the questions on Matthew’s fourteens and on the kings he omits). So the two lists also differ in length; neither writer meant them to match name for name.

Christian scholars are still divided between these explanations, and no ancient source settles the matter; Africanus admitted that he could ‘urge no testimony in its support’ beyond family tradition. John Gill cited a passage in the Jerusalem Talmud that speaks of ‘Mary the daughter of Eli’ in support of the view that Luke gives Mary’s line, but whether it refers to Jesus’ mother is disputed. Both lists also name a Shealtiel (Salathiel) and a Zerubbabel, and most commentators take them to be the same men in both, though some think them different men with the same names.