The believer, who feels himself offended by another, should approach him alone so that he knows and has a chance to apologize and ask forgiveness.
It is not what we do naturally. When offended, our nature resents against the offender, and we seek revenge proclaiming to others the evil that he did to us, thus spreading evil. Alternatively, we just hope that the offender might come to us asking for forgiveness.
However, the commandment of the Lord is wise, and aims to re-establish peace immediately, avoiding a "root of bitterness", a sin that brings serious consequences in the church if not corrected soon. Often the offender has not realized he has caused offense, unintentionally, or it happened in a moment of strong irritation, and he immediately undoes the misconception and sincerely apologizes. Peace will then return between the two.
Nevertheless, the offence may have been intentional. The offender will still have the opportunity to repent and recant for having sinned against a brother. If he caused any damage, he must demonstrate his repentance by apologizing to him and doing the necessary repairs. If that happens, the case can be closed and peace will return between them, without harmful repercussions. With this peaceful solution, the offended will have "won his brother".
Sadly, this does not always happen, the offender does not want to admit that he caused the offence, or persists in the attitude of harming his brother who complained to him. Again, the natural tendency of the offended is to somehow obtain revenge, and defame and vilify the offender. However, this is not what the Lord said he ought to do: he should go and talk to the offender again, taking one or two people with him to serve as witnesses.
Those attending will hear both sides of the controversy, maybe resulting in a reconciliation at this point. However, if the offender maintains his aggressive attitude and does not recognize his sin, his companions will serve as witnesses so the case may be brought to the church for judgment. The Law of Moses required the use of witnesses at the trial of the accused (Deuteronomy 19:15).
The need for witnesses is often forgotten when bringing contentious cases before the church, thus resulting sometimes in unfair judgments. In 1 Corinthians 6:1-8 we read that in the church of Corinth they were not practicing this teaching of the Lord: a brother was going to law against another to be tried by unbelievers. Paul warned the church that this was shameful as it meant that there was no wise man within the church, if the offended had to seek justice from those that are least esteemed by the church (v. 4-6). To go to court against a brother already brings defeat, even before the case is tried. It is better to suffer injustice and bear the injury (v. 7).
If the offender listens and submits to the judgment of the church there will be peace, although the case becomes public. However, if he does not want to listen to the church, he must be regarded as "Gentile and publican", in other words, someone who is outside of the communion of the church: his attitude is of sin, because having offended a brother he refuses to repent and do reparation after having been proved guilty.
If he is a true believer, he will not lose his salvation, because salvation is eternal, and he will continue within the church of Jesus Christ. However, he will not be received in the local church until he repents and makes amends. Otherwise, he will be a "root of bitterness" to the assembly. It is a discipline that must be applied to all who live in sin (1 Corinthians 5:11) that he be delivered “to Satan for the destruction of the flesh, that his spirit may be saved in the day of the Lord Jesus” (1 Corinthians 5: 5). The purpose is to make him wise to his situation, repent and abandon sin.
The Lord Jesus then repeated the words He had earlier told Peter (chapter 16:19): "whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven", this time addressed to all His disciples, in the context of discipline in the church. The action of the church disciplining a believer who lives in sin by interrupting fellowship with him, has the approval of God, as well as the action of welcoming him back again in communion when he leaves his sin.
With these words, the Lord Jesus declares He authorizes the church to impose sanctions on those who assemble in it, i.e. it can use disciplinary measures that might seem to be contrary to Christian love, but in reality, they conform to the desire of the local assembly to maintain purity within itself and to correct those who are impure.
The question then arises: what is the minimum number of members that a church must have in order that it may exercise that authority? The answer comes soon after, two or three gathered in the name of the Lord Jesus!
Verse 19 may be applicable to response to prayers when there is agreement between two disciples on a request. In this case, it is that of prayer made collectively (more than one believer asking the same thing, or just one with the "Amen" declared by the others).
However, there are several other conditions for prayers to be heard by God, whether collectively or individually, as for example:
In its context, which is more to the point, the teaching is that it only takes two believers go to God in prayer with respect to discipline in the church, to ensure they will be heard. Even if the victim and the offender were to agree to ask for God's guidance about their strife, God will hear them!
Meet "in the name of the Lord Jesus" simply means:
Authorized by Him: He gave permission to all who belong to Him to gather in a local assembly to, in His place, grow spiritually together as if they were Himself - His body.
Always recognising that He is Head of this body, all being done by Him and for Him.
No group can arrogate for itself the privilege of being the only "church" here on earth, to the exclusion of all other believers who do not assemble with them.
There is a plethora of congregations who meet "in the name in the Lord Jesus" and fulfil these conditions, but they vary widely in understanding and practicing biblical doctrines, many following ancient traditions with little or no biblical basis.
However, we all belong to Christ, if we were saved by the grace of God solely through faith in His Person and in His vicarious work on the Cross of Calvary. In chapters 2 and 3 of Revelation, we read of seven churches, all different from each other in many ways, but they were all churches of Christ.
There is no justification for the unfortunate exclusivity found in many of them, refusing to have fellowship with other brothers just because they do not assemble with them, or in the same way they do. Such exclusivity is often adopted because of fear that their own tradition might be exposed as defective and to find that there are better ways than their own to obey and serve the Lord.