After three straight questions aiming to trap him, Jesus now asks the Pharisees one of his own. The question is probably designed to make them think about Jesus in a new light. It is part of the invitation to the banquet.
Jesus wants to discuss the terminology “Son of David”. This term is used quite a bit in Matthew, so it should not be seen as incorrect, but Jesus wants to examine it more closely.
The problem is with the image created by the term “Son of David”. At this time in Israel’s history there was a growing belief in and desire for a messiah, a Christ. As the Son of David, this figure was seen as a conquering hero, like David himself, The Roman hand was heavy and the hoped for messiah would push out the Romans from the land and reestablish Israel as an independent power. This will explain why the Roman leadership in the region, and their temple leader puppets, were death on messianic movements. They were seen as revolutionary.
But Jesus uses Psalm 110 to show that the idea of the messiah is bigger than what people were looking for. The people wanted another David, one whom David could call son. But Psalm 110 shows a messiah that David would call Lord, one at the right hand of God himself.
Jesus is saying to the Pharisees, “Your messiah is too small.”
Psalm 110 was used quite a bit in the early church as a picture of Jesus after the resurrection and ascension. Apparently it had enough of a reputation as a messianic psalm even with the Pharisees that Jesus could use it in this manner.
Jesus embodied this type of messiahship during his earthly ministry. He was a spiritual leader, not leading a revolution against Rome. However, he will die as a revolutionary anyway.
Jesus was hard on the Pharisees. This is because they were closer to the kingdom than any other group in the land. But most of them rejected his invitation. Here, as in previous encounters, they reacted by leaving him rather than following him.
The time for questions is over. Jesus will now deliver his farewell speech to Jerusalem.