Then will I teach transgressors your ways; and sinners shall be converted unto you.
Read Chapter 51
Augustine of Hippo
18. But see what he annexeth: "With Principal Spirit," he saith, "confirm Thou me." Wherein "confirm"? Because Thou hast pardoned me, because I am secure, that what Thou hast forgiven is not to be ascribed, on this being made secure and with this grace confirmed, therefore I am not ungrateful. But I shall do what? "I would teach unrighteous men Thy ways" (ver. 13). Being myself of the unrighteous (that is, one that was myself an unrighteous man, now no longer unrighteous; the Holy Spirit not having been taken away from me, and I being confirmed with Principal Spirit). "I would teach unrighteous men Thy ways." What ways wilt thou teach unrighteous men? "And ungodly men to Thee shall be converted." If David's sin is counted for ungodliness, let not ungodly men despair of themselves, forasmuch as God hath spared an ungodly man; but let them take heed that to Him they be converted, that His ways they learn. But if David's deed is not counted for ungodliness, but this is properly call ungod...
Thee. The sinner cannot testify his gratitude better, than by promoting the conversion of others. (Worthington)
This is a sort of satisfaction. (Menochius)
While engaged in sin, David could not well exhort his subjects to repentance. His example was rather an inducement for them to transgress. (Berthier)
But when they saw his grief, and knew that God had pardoned him, they were no longer tempted to despair. He also watched more carefully over their conduct.