Without a fuller understanding of the context and ways of teaching in the times when Jesus was alive, this is a very difficult passage to comprehend. However, it would have been perfectly understandable to the crowds amassing in Jerusalem.
Firstly, we must accept that 'the Christ' in Greek or 'the Messiah' in Hebrew means 'God's anointed One'. In ancient times, a man was made King by being anointed with oil. So, when Jesus spoke of the scribes determining that the Christ is the son of David, He isn't directly referring to Himself. He is stating more generally when He asks the question: ''How can the scribes say that God's anointed King who is to come is the son of David?'' And to support His argument, Jesus quotes from Psalm 110 v 1, which the Jews believed to be a prophetic Psalm referring to the Messiah who was to come. Jesus goes on to ask, ''If this Messiah is David's son, then how can David address him as Lord?''
It may either appear very confusing to you or perfectly simple, but the bigger question here is: 'What is Jesus seeking to teach?' The commonest title for the long-awaited Messiah was 'Son of David' and Jesus was often addressed using this form, especially by the crowds. Just a couple of chapters ago in this Gospel, we see it- Mark 10 v 47, by blind Bartimaeus. The genealogies at the beginning of the Gospels of Matthew and Luke, although different, cite that Jesus was of the line of David, and Jesus is in agreement with them: it is not that Jesus denied being the son of David, but that He claimed to be not only that, but David's Lord! Jesus is again attempting to extricate Himself from the Jewish stereotype that their Messiah would be an earthly conquering King. He came not to bring in an earthly Kingdom, but a heavenly one!
We can learn from this difficult passage that Jesus made it clear to those who had ears to hear-and there would have been those in the crowds-that He was sent for a different purpose than expected. In the light of events to come shortly after this, we may say that He failed, but He made it as clear to the Jews as possible by using Bible passages central to their understanding and demonstrating that they did not mean what they had believed them to mean. So hungry were they to throw off the shackles of Roman oppression they were blind to Scripture and the Truth.
Is there anything in your life which threatens to distort the truth about God to you?