So the Gospels of Matthew, Luke and John all had genealogies. Why doesn’t Mark?
Each of the four Gospels was written for an explicit purpose, and the genealogies given focus in that direction.
Matthew was written to the Jews to show them the Messiah, the Lion of the Tribe of Judah beginning with the first covenant, Abraham. Because Matthew could take shorthand, he wrote down a lot of what Jesus said verbatim.
Luke was written to the Greek to show Jesus as fully Man beginning with the first man, Adam. Being a physician, Luke focused on what Jesus felt.
John was written to the Church to show Jesus as fully God. This book focuses on Jesus’ identity as the pre-existent one.
Mark was written to the Romans. It focuses on what Jesus did. Jesus is perpetually on the move doing this or that. He’s serving people and helping out. Mark portrays Jesus as a servant. Back in the day, no one cared about the lineage of a servant, so Mark has no genealogy.
Source: Missler, Chuck. The Book of Matthew: A Commentary. Koinonia House.