Even in his failings—the affair with Bathsheba, most famously—David has become the prototype of repentance and divine forgiveness.
But as Christians, we accept the notion of a sinful nature and the need for repentance and redemption.
How are they representing the views of the Bible, that humility and repentance are virtuous and that pride goes before a fall?
c.1300, from Old French repentance "penitence" (12c.), from present participle stem of repentir (see repent).
Repentance goes beyond feeling to express distinct purposes of turning from sin to righteousness; the Bible word most often translated repentance means a change of mental and spiritual attitude toward sin. [Century Dictionary]
There are three Greek words used in the New Testament to denote repentance. (1.) The verb _metamelomai_ is used of a change of mind, such as to produce regret or even remorse on account of sin, but not necessarily a change of heart. This word is used with reference to the repentance of Judas (Matt. 27:3). (2.) Metanoeo, meaning to change one's mind and purpose, as the result of after knowledge. This verb, with (3) the cognate noun _metanoia_, is used of true repentance, a change of mind and purpose and life, to which remission of sin is promised. Evangelical repentance consists of (1) a true sense of one's own guilt and sinfulness; (2) an apprehension of God's mercy in Christ; (3) an actual hatred of sin (Ps. 119:128; Job 42:5, 6; 2 Cor. 7:10) and turning from it to God; and (4) a persistent endeavour after a holy life in a walking with God in the way of his commandments. The true penitent is conscious of guilt (Ps. 51:4, 9), of pollution (51:5, 7, 10), and of helplessness (51:11; 109:21, 22). Thus he apprehends himself to be just what God has always seen him to be and declares him to be. But repentance comprehends not only such a sense of sin, but also an apprehension of mercy, without which there can be no true repentance (Ps. 51:1; 130:4).