David flew into a rage against the man, and said to Nathan, 'As the Lord lives, the man who did this deserves to die! He shall pay for the lamb four times over, because he did such a thing and showed no pity.' And Nathan said to David, 'That man is you!' (2 Samuel 12:5-7)
The intensity of David's rage directed toward the rich man seems disproportionate to his crime. J. P. Fokkelman elucidates:
I Have Sinned Before God >>
David does not react as a good judge. His quickness, severity and intense indignation exhibit his plagued conscience and lack of equilibrium. The force which enables him to consummate the absolute act of murdering Uriah is the selfsame force which enables him to commit the absolute act of imposing the death penalty upon the rich man.
The great satisfaction which David hopes to gain by the condemnation of another is meant to fill the emptiness brought about in David's soul by Uriah's liquidation... It is not difficult to reprehend this David. It is tempting to elevate oneself by being indignant about so much evil, but then one is doing the same thing as David in regard to the rich man. Nathan takes a different approach. Before confronting David with his dark side he lets him see his good side.