From "Answers To Your Bible Version Questions" ©2003 David W. Daniels
Reproduced by permission
Question: Why Are Matthew's and Luke's family trees of Jesus different?
Answer: There are two genealogies in the New Testament. Both of them are accurate. Both are intended to show the Lord Jesus Christ is indeed the Son of David to rule over Israel as its final and eternal King.
The Luke genealogy is that of Mary, and is rather complete. The Matthew genealogy is that of Joseph, and it is arranged for easy memorization and is abbreviated.
Some will point out the fact that Hebrew letters also represent numbers, and the name David adds up to fourteen. Regardless, Matthew counts in fourteens for easy memorization or easy reference to Jesus' genealogy through Joseph. The Old Testament provides the names that are in between, except for those after the Babylonian captivity.
Matthew uses this literary device of grouping things in sevens throughout his gospel. Doing that here makes it easier to remember the line leading to Jesus, using what some say is twice the divine number seven, or fourteen. In other words, while Matthew listed some of the main players, generation by generation, he intentionally skipped some generations to make the list easy with fourteens to count three times.
There are other questions regarding using names that are not biological, but legal parents. Matthew uses the custom of the day to list genealogy, not always by father and son, or father and grandson, but sometimes the legal father, ignoring the biological father.
The bottom line is this, Matthew lists Jesus' legal lineage through Joseph, who is not His biological father, anyway. But Luke lists Jesus' physical ancestry down to Mary, who literally carried Him in the womb, and thus was His mother. This all shows that Jesus is the legal and literal Son of David, qualified to reign over Israel.