Your question bothered the early Church Fathers who probably added the words found in Luke 3:23 "as was supposed." They also spent lots of energy trying to reconcile the obvious differences in these two accounts of Jesus' ancestry. Your question also speaks to one of the many contradictions that are found in the Bible.

I think it is fair to say that the genealogies serve different purposes in the two gospels you mention. It was important to Matthew to link Jesus with the history of the Jews so he begins his genealogy with Abraham and works through the royal line of the Kings of Judah. On the other hand, Luke, who appears to have been born a gentile and to have converted first to Judaism and then to Christianity, begins with Joseph, the earthly father of Jesus and works backward until he arrives at Adam, the presumed father of all humanity, which, of course, included the Gentiles. Luke also ignores the royal line of the Kings of Judah, once he gets past David. He traces the line from David to Nathan (see Luke 3:31). Indeed a comparison of the two genealogies (Matthew 1 and Luke 3) reveals that they do not agree in many details.

These early Christians defined God as a Being who was outside of life. When they believed they experienced God in Jesus, they had to explain how this external Being got into this human Jesus. The Virgin Birth was one way two of them, Matthew and Luke, addressed that question. You will not find a miraculous birth tradition in Paul, Mark or John. But Matthew and Luke, the authors of the Virgin tradition, also wanted people to know that Jesus was fully human. The genealogies served well that purpose. This explanation doesn't really close the circle on all the dimensions of the God people believed that they met in Jesus but no human definition of the Holy ever does.

John Shelby Spong