One part of understanding this line is the scene itself; the other part is to notice this is after the vineyard and wedding parables and before ch 23.
We know that Judaism was looking for David's son to appear because of all the MAD/D'ist people here obsessed with that. (D'ism is a way of doing Judaism with a modern twist). So it was logical in Mt 22:42 to do a climactic come-back to Judaism, to all its pesky questions. 'What do you (Judaism) think about the Christ? Whose son is he?'
We know the answer.
But this is not what Ps 110 is saying. The psalm is saying that he is the Lord of the universe, and David's lord. So he can't just be David's son as they knew it.
That is the whole point. Christ is not then nor in the future to be that kind of son. It is not what those passages were about. They were shadows or copies or 'types' of the reality that was coming in Christ. D'ism and MAD, like Judaism, are stuck in the former.
By the way, he won. I'm not sure if D'ism gets that.
Then came ch 23, the blast on Judaism, which ends with the declaration that the 'house' is already desolate (the term from Dan 9, which pops up again in 20 verses), except for those who sing Psalm 118 about him.
THE SETTING
But we can't forget that this comes after the general dismissal of Judaism in 21's vineyard parable and 22's wedding parable. The vineyard parable was 'talking about them.' He said another 'ethne' was going to take the place of Judaism. Not just take the place either. There would be destruction. There was going to be a king whose wedding invite was chided. The refused king sends his ARMY and BURNS down the city of the refusers. It was a pretty rough week for Judaism in general.
And now this--this denunciation of their doctrine of the son of David, which is what our friends here think is still going to happen. Apparently they can accuse people of making God a liar, but if God punishes a whole city for the wrong 'son of David' and then blesses that city X000 years later for the wrong son of David, it's OK. Yeah, right.