Infidels.org calls this a contradiction and asks the question, "Who is the father of Joseph?"
|“|| Matthew 1:16 And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ.
Luke 3:23 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.
That Matthew 1 and Luke 3 differ in their genealogies is a well-known fact. As observed by the Halley's Bible Handbook note for Matthew 1:1-17, the Matthew genealogy goes back to Abraham and Luke to Adam, Matthew starts at the beginning and Luke at the end, and from David to Jesus they present different lines of descent. As Halley's further notes:
|“|| "The commonly accepted view is that Matthew gives Joseph's line, showing Jesus to be legal heir to the promises given to Abraham and David, and that Luke gives Mary's line, showing Jesus' blood descent: 'who as to his human nature was a descendant of David' (Romans 1:3). Mary's genealogy, in accordance with Jewish usage, was in her husband's name. Joseph was the son of Heli (Luke 3:23)-that is, Heli's son-in-law. Jacob was Joseph's father (Matthew 1:16)."
-Halley's Bible Handbook
This has been recognized since at least 1917 when the Scofield Reference Bible printed a similar explanation:
|“|| "In Matthew, where unquestionably we have the genealogy of Joseph, we are told Matthew 1:16, that Joseph was the son of Jacob. In what sense, then, could he be called in Luke 'the son of Heli'? He could not be by natural generation the son both of Jacob and of Heli. But in Luke it is not said that Heli begat Joseph, so that the natural explanation is that Joseph was the son-in-law of Heli, who was, like himself, a descendant of David. That he should in that case be called 'son of Heli' ('son' is not in the Greek, but rightly supplied by the translators) would be in accord with Jewish usage.(CF) 1 Samuel 24:16 The conclusion is therefore inevitable that in Luke we have Mary's genealogy; and Joseph was 'son of Heli' because espoused to Heli's daughter. The genealogy in Luke is Mary's, whose father, Heli, was descended from David."
-Scofield Reference Bible
Again, it accords with Jewish usage to present the mother's genealogy in the father's name, thus the confusion over two seemingly differing genealogies. It also explains why the Luke account begins with a focus on Mary, giving detail only she would know, detail specific to her life. Luke ch. 1 delves into the history of Mary's cousin Elisabeth and Elisabeth's child, John the Baptist, the angel's greeting of Mary, Mary's thanksgiving to God, and how Mary stayed with Elisabeth afterward. Luke 2:19 says, "But Mary kept all these things, and pondered them in her heart." Luke 2:34 records Simeon speaking to Mary specifically, while Luke 2:48 records her conversation with Jesus.
In short, a logical reading of Luke shows the narrator of the early chapters appears to be Mary, not Joseph, and seems to be written from her point of view distinctly. Matthew 1, on the other hand, tells a more matter-of-fact account from Joseph's point of view, telling detail from his vantage point and only that pertaining to him. Just as Luke relates Mary's feelings and thoughts, so does Matthew's early account with Joseph. Matthew 1:19-20 describes Joseph's thought process to send Mary away privately, and his discussion with the angel that persuades him otherwise. Matthew 2:19-23 describe the angel's message to Joseph specifically that it's alright to return to Israel.
Just as the early chapters of Matthew appear written from Joseph's view, so the early chapters of Luke appear clearly written from Mary's, and the genealogies in Matthew those of Joseph's while Luke records Mary's genealogy.
Furthermore, it should be pointed out that the Greek word huios translated "son" can simply mean descendant, so Jesus was called the descendant of Heli, not Joseph. The following are examples where the same word translated "son" in Luke 3:23 is used in a broader sense to refer to descendants:
|“|| Luke 3:23 And <kai> Jesus <Iesous> himself <autos> began <archomai> to be <en> about <hosei> thirty <triakonta> years of age, <etos> being <on> (as <hos> was supposed <nomizo>) the son <huios> of Joseph, <Ioseph> which was the son of Heli, <Heli>
Matthew 1:1 ¶ The book <biblos> of the generation <genesis> of Jesus <Iesous> Christ <Christos>, the son <huios> of David <Dabid>, the son <huios> of Abraham <Abraam>.
Matthew 1:20 But <de> while he <autos> thought on <enthumeomai> these things <tauta>, behold <idou>, the angel <aggelos> of the Lord <kurios> appeared <phaino> unto him <autos> in <kata> a dream <onar>, saying <lego>, Joseph <Ioseph>, thou son <huios> of David <Dabid>, fear <phobeo> not <me> to take <paralambano> unto thee <sou> Mary <Maria> thy wife <gune>: for <gar> that which is conceived <gennao> in <en> her <autos> is <esti> of <ek> the Holy <hagios> Ghost <pneuma>.
Matthew 9:27 ¶ And <kai> when Jesus <Iesous> departed <parago> thence <ekeithen>, two <duo> blind men <tuphlos> followed <akoloutheo> him <autos>, crying <krazo>, and <kai> saying <lego>, Thou Son <huios> of David <Dabid>, have mercy <eleeo> on us <hemas>.
Matthew 27:9 Then <tote> was fulfilled <pleroo> that which <ho> was spoken <rheo> by <dia> Jeremy <Ieremias> the prophet <prophetes>, saying <lego>, And <kai> they took <lambano> the thirty <triakonta> pieces of silver <argurion>, the price
- Meritt, Jim (1992). A list of Biblical contradictions. Retrieved from http://www.infidels.org/library/modern/jim_meritt/bible-contradictions.html.
- Halley, H.H. (1984). Halley's Bible handbook with the New International Version. Zondervan Publishing House.
- Scofield, C.I. (1917). Scofield Reference Notes.
- Thayer and Smith. Huios. The New Testament Greek Lexicon.