“Never let us be discouraged with ourselves; it is not when we are conscious of our faults that we are the most wicked: on the contrary, we are less so. We see by a brighter light. And let us remember, for our consolation, that we never perceive our sins till He begin to cure them.” Francois Fenelon (1651-1715)
We are not a race of people happy to have our faults shown to us. It seems to be one of the primary elements of our sin nature. We don't enjoy being wrong. We don't enjoy having faults and I know of very few people who enjoy having someone else point this out.
It was this way from the start. In the first recorded conversation between God and Adam in Genesis 3:8-12, Adam's reaction to God's question if he had about what he had done (eaten from the forbidden tree) was to blame Even and even imply it was God's fault (this woman you gave me).
This is what is often called a "natural" reaction to being confronted with doing wrong. When my kids were little I often wondered when we had adopted those two orphan children named "Aidunno" and "Knotme" were the ones responsible for any broken toy, marks on the walls, dirt on the rug or mess not cleaned up.
But this Christian life calls for us to fess up. Part of our salvation experience is predicated on our open awareness and admission of our sinfulness to the point we could not save ourselves. This is not just a "well no one is perfect" attitude, but one of acute awareness that we are an eternity away from coming even close to meeting the standard that is Christ. If we could, we would not need a Savior.
A Christian Response to a sin being pointed out is not one of blame-shifting or argument or even avoidance, but one of humble acknowledgement, repentance, and asking God, relying upon God, to help you turn from this sin.
Our sins should not be a source of discouragement but one of encouragement because we are see the work of the Father in our lives. This is a source of joy, knowing that our Father, through Christ, is molding us back into that image of Him he originally created us to be.