The answer
St. Matthew's focus group was the Jewish people. He traced the genealogy of our Lord through two categories of fourteen generations each. His goal was to prove to the Jewish nation that our Lord Jesus Christ is indeed the Messiah, the Son of David, who had the legal rights to David's throne as promised.
St. Luke, the historian, presented the genealogy of our Lord with careful details based on his interviews with the Holy Virgin, St. Mary. This genealogy is traced through her lineage. However the divergence does occur in two places. St. Matthew identified the biological father of St. Joseph as Jacob and traced St. Joseph lineage's back to Solomon, son of David. By keeping the tradition of marrying the widow of a deceased brother, St. Joseph was also referred to as son of Heli (who died without having sons). This account places St. Joseph as son and subsequently son-in-law of Heli. The second inference is identified in St. Luke's account. He traced the lineage through St. Mary, which also mentioned Heli and continued with her lineage back to Nathan, son of David.
Both St. Matthew and St. Luke infer that although our Lord Jesus Christ is the presumed legal son of St. Joseph, He is in fact the Son of Mary.
"Now Jesus Himself began His ministry at about thirty years of age, being (as was supposed) the son of Joseph, the son of Heli" (Luke 3:23).
"And Jacob begot Joseph the husband of Mary, of whom was born Jesus who is called Christ" (Matthew 1:16).
Answered by His Eminence Metropolitan Youssef (opens in a new tab)