The sacraments are all instituted by Christ and can be found in the Bible. However, the way that these sacraments are to be conveyed is not necessarily in the Bible.
The form that they took on is one of development over several hundred years. Jesus gave many special powers to his Apostles, but he did not necessarily tell them step-by-step how it was to be carried out or it is that it was not documented in the Bible. It is possible that he did tell them, but it is not written in the Holy Scriptures (John 21:25).
Therefore, those that believe that the only authority for Christians is Scripture and disregard all traditions are missing an aspect of true Christianity.
Regardless, the Sacrament of Reconciliation and Penance is a very important one and it is also one that is often misconstrued by those who do not understand it or where it came from. John 20:21-23 is, for the most part, the main supporting verse for Confession. Jesus had bestowed a power on his disciples of forgiving or retaining sin, which was previously reserved to God alone, and technically still is!
One thing to keep in mind is that our present day priests and bishops are the successors of the Apostles. In all reality Jesus was speaking to a group of ordained priests and bishops, the ones that Jesus chose! This group was the first group to be ordained. Jesus himself ordained them! Holy Orders is the process through which men are ordained to the priesthood.
Catechism of the Catholic Church paragraph 1461 is a good passage on learning the Church’s official teaching on Confession. Reading onward to #1462 and others is also helpful. Paragraph 1461 has its roots in Scripture. It references John 20:21-32 and also 2 Corinthians 5:18.
“Since Christ entrusted to his apostles the ministry of reconciliation, 65 bishops who are their successors, and priests, the bishops’ collaborators, continue to exercise this ministry. Indeed bishops and priests, by virtue of the sacrament of Holy Orders, have the power to forgive all sins ‘in the name of the Father, and of the Son, and of the Holy Spirit.'” -Catechism of the Catholic Church #1461
In 2 Cor. 5:11-21 is what is called “The Ministry of Reconciliation.” To reconcile means, “to reestablish a close relationship between.” This passage explicitly helps to show the role of the priest or bishop in the sacrament. Here I will quote verses 16-20:
“Consequently, from now on we regard no one according to the flesh; even if we once knew Christ according to the flesh, yet now we know him so no longer. So whoever is in Christ is a new creation: the old things have passed away; behold, new things have come. And all this is from God, who has reconciled us to himself through Christ and given us the ministry of reconciliation, namely, God was reconciling the world to himself in Christ, not counting their trespasses against them and entrusting to us the message of reconciliation. So we are ambassadors for Christ, as if God were appealing through us. We implore you on behalf of Christ, be reconciled to God.”
In this passage, Paul is describing his ministry and the ministry of all the Apostles. He shows how he has power to forgive sin in the name of Christ. He also describes the role of the priest. Let’s do a verse-by-verse exegesis.
Verse 16 speaks of how the disciples came to know Christ through the flesh yet they do not know him now as such. They know Christ in the Spirit. New American Bible footnotes clearly convey the meaning:
“[16-17] Consequently: the death of Christ described in 2 Cor. 5:14-15 produces a whole new order (2 Cor. 5:17) and a new mode of perception (2 Cor. 5:16). According to the flesh: the natural mode of perception, characterized as “fleshly,” is replaced by a mode of perception proper to the Spirit. Elsewhere Paul contrasts what Christ looks like according to the old criteria (weakness, powerlessness, folly, death) and according to the new (wisdom, power, life); cf 2 Cor. 5:15.21; 1 Cor. 1:17-3:3. Similarly, he describes the paradoxical nature of Christian existence, e.g., in 2 Cor. 4:10-11,14. A new creation: rabbis used this expression to describe the effect of the entrance of a proselyte or convert into Judaism or of the remission of sins on the Day of Atonement. The new order created in Christ is the new covenant (2 Cor. 3:6).”
Verse 17 talks about people that are baptized. “Whoever is in Christ is a new creation” refers to what happens at baptism. People are not merely putting on Christ; they are born again in Christ. They become one in Christ and with the rest of the baptized believers. Similar symbolism is seen 3 verses earlier when verse 14 says, “one died for all; therefore, all have died.” In baptism we die in Christ and are born again in Christ just as Christ had died on the cross and put sin to death and arose in newness of life. Baptism puts to death our old sin and we are regenerated as a child of God and no longer just a creature of God.
In verse 18 Paul praises God and gives authenticity to his power by saying that his powers and ministry are from God. When Paul speaks of being “reconciled to God through Christ” he speaks of being made one with others through the sacrifice of Christ. Then Paul tells us this special power that was given to him by God and that it is the “ministry of reconciliation.” (Cf. John 20:21-23).
Verse 19 goes on to say that God sent his only Son to bring the world to unity under God no matter who they were, Jew, Gentile, etc, and from Christ that message was to be carried on by his disciples. The way (message) of reconciliation was entrusted to those specific people, the ones sent by Christ, and their appointees.
Verse 20 describes the exact role of the priest: “ambassadors for Christ, as if God were appealing through us.” This is exactly what happens at confession. The priest is not the “mediator” between God and the confessor in the sense that anti-Catholics think. No, the priest is an ambassador for Christ, as if God were appealing through them.
This is the same role that is understood in the title “Vicar of Christ” for the pope. It’s not that the pope is equal to God in any form; it’s that he is standing in for him as an ambassador. God uses the priest as a fill-in for him, a physical sign that one’s repentance is being heard and that one hears for sure that their sins are being absolved. The word ambassador means “official representative of the highest rank.” The priest is a representative of God, more specifically Jesus. Paul moves on to motivate people to repent.
His exact words are, “on behalf of Christ.” In that statement he is exercising his ambassadorship. Then, he wants them to repent because that is what God wants, “be reconciled to God.” That means to be unified as a people with one belief under the one, triune God.
Verse 21 Paul explains God’s love for us in that he sent his only Son to become flesh (sin) and be just like us, “so that we may become the righteousness of God in him.”
Paul knows, as an appointed Apostle, of his role in the Church and all of the power bestowed upon him. Even in the First letter to the Corinthians he expresses this point. After telling the people in Corinth that this is all for Christ and not done in the name of humans he tells us in Chapter 4 that “Thus one should regard us: as servants of Christ and stewards of the mysteries of God.”
In other words, the disciples are to been seen as and thought of as God’s caretakers of his plan of salvation as handed to Christ to his disciples. They are the managers of the mysteries of God. So, the one’s appointed by Christ and their appointees (Paul was an appointee) are ambassadors for Christ and stewards of his mysteries, the exact same thing that the priests of today exercise.