While all four of the Gospel writers seem to highlight the threefold office of Christ (Prophet, Priest, and King), it has struck me this Advent season how the synoptic Gospels each appear to emphasize one specific office in the way each introduces Jesus.
Matthew - Priest
Although it could be argued that Matthew emphasizes Jesus' kingly office by beginning with a genealogy that places him in the royal line of David, it is here (and here only) that we learn why this holy Child is to be named Jesus. "She will bear a son, and you shall call his name Jesus, for he will save his people from their sins" (Matthew 1:21). His name is tied to the priestly sacrifice he will offer for his people's sins - for that is how he will save them.
Mark - Prophet
The Gospel of Mark does not include a birth narrative of the Christ Child. Instead, Jesus comes onto the scene at the beginning of his public ministry. And the first time we hear him speak, he is fulfilling his prophetic office (preaching about the kingdom). "Now after John was arrested, Jesus came into Galilee, proclaiming the gospel of God, and saying, 'The time is fulfilled, and the kingdom of God is at hand; repent and believe in the gospel'" (Mark 1:14-15).
Luke - King
When Luke tells about the angel Gabriel visiting Mary, he emphasizes what Gabriel says regarding the kingly office of Mary's Child. "He will be great and will be called the Son of the Most High. And the Lord God will give to him the throne of his father David, and he will reign over the house of Jacob forever, and of his kingdom there will be no end" (Luke 1:32-33).
As stated earlier, no one Gospel is limited to one of Christ's offices. And just because the Synoptics begin the way they do does not mean they only emphasize that particular office. For instance, Matthew goes on to emphasize the prophetic office of Christ with the Sermon on the Mount and with the five major sections of teaching included in his Gospel (reflecting the five books of Moses and showing that Jesus is the ultimate fulfillment of Moses' prophetic office). In addition, his Gospel has more parables about the kingdom than any other - and there is little doubt who the King is!
But it is interesting to see how Jesus is introduced in these three Gospels, and it seems that each emphasizes one of Christ's three offices - Prophet (Mark), Priest (Matthew), and King (Luke).