Church Fathers on Matthew 22:43

The Jews tempted Christ, supposing Him to be mere man; had they believed Him to be the Son of God, they would not have tempted Him. Christ therefore, willing to shew that He knew the treachery of their hearts, and that He was God, yet would not declare this truth to them plainly, that they might not take occasion thence to charge Him with blasphemy, and yet would not totally conceal this truth; because to that end had He come that He should preach the truth.

He first asked His disciples what others said of Christ, and then what they themselves said; but not so to these. For they would have said that He was a deceiver, and wicked. They thought that Christ was to be mere man, and therefore 'they say unto Him, The Son of David.' To reprove this, He brings forward the Prophet, witnessing His dominion, proper Sonship, and His joint honour with His Father.

This passage is out of the 109th Psalm. Christ is therefore called David’s Lord, not in respect of His descent from him, but in respect of His eternal generation from the Father, wherein He was before His fleshly Father. And he calls Him Lord, not by a mere chance, nor of his own thought, but by the Holy Spirit.