Begat's Bewrong!

St. Matthew 1:16 says, " And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ" Back the truck up! I thought God was the daddy? What does it matter if Joseph was descended from David if he isn't the legitimate father. Why doesn't it mention who Mary was descended from. This is the first error in the New Testament and one that has been VERY creatively justified.