At the words "through my fault," we strike our breasts. Why? In the ancient world, striking one’s breast was a sign of mourning.
At Jesus’ death on the cross, the Gospel of Luke recounts that the crowd returned to their homes "beating their breasts" (Luke 23:48). Zechariah the prophet had prophesied that the inhabitants of Jerusalem would do this when he said, "When they look on him whom they have pierced, they shall mourn for him, as one mourns for an only child" (Zechariah 12:10).
Our sins are our death warrant. We beat our breasts as we declare our sinfulness in the Confiteor in imitation of the tax collector who, "standing far off, would not even lift up his eyes to heaven, but beat his breast, saying, 'God, be merciful to me a sinner'" (Luke 18:13)
Hence, we need to perform this act as a symbol rather than for show.