Here is another of those Proverbs that seems to directly contradict what has been said in the previous verse. Here it has to do with arguing your case with your neighbor. But the thing that truly helps us to understand this proverb is that it deals with arguing your case with your neighbor "alone." The ESV and the KJV bring this out.
When a person has a conflict with another person, the best way for it to be resolved is for the two of them to get together and to work it out between them. This is what the writer of Proverbs is saying here. This proverb has to do with gossip more than anything else. When there is a conflict, take the conflict to the person with whom you have the conflict - and no one else. That is what the writer is saying when he says not to reveal the secret of another. When there is a conflict, we don't need to reveal that we have had one with everyone else. That is usually what happens when there is a fight. We decide to talk with everyone else - telling them about everything that has happened and every way that this other person has hurt us - or has wronged us. That is revealing the secret of another.
Here is a concept that I know is foreign to the church today. When we have a fight or disagreement with someone - that situation is to be treated as if it is a secret between us and the person with whom we've had the disagreement. It is to remain that way - until we've worked it out with that person. The reason we should do this is because God will give us grace - and give the person with whom we have the disagreement grace. But anyone we bring into the situation - will not have grace to deal with it. They will tend to take one side or the other - and soon factions will begin to develop.
When the person with whom we have the disagreement begins to hear that we've told others - new problems will develop. The passage here says that when the person with whom we've had the argument hears that we're talking to others about it - they will reproach us for doing it. There is an additional offense when this happens. There are already problems with this person - but now they feel that they are being slandered with gossip.
Now the next step in all this is that the argument begins to develop into a full-sized war. They begin to send out an evil report about you. They are so offended that you've begun to gossip, that they begin to gossip as well. Just as you decided to share the worst of your disagreement with others - they do the same. You feel greater offense but what they are doing is only what you've already done to them. The sad reality with this entire situation is that it will continue toward greater and greater bitterness until one or the other involved with be Christlike enough to humble themselves and begin working toward true healing. This involves actually talking about the problem to the person with whom you have the problem. What is so sad is that the vast majority of the time all that happens is that the two people eventually move to an uncomfortable silence between them. Their relationship becomes superficial - awaiting the next blow up that will come in the future.
Argue your case with your neighbor alone. That is wisdom. It will bless you - and honestly - it will bless your church as well. This would be such a cause for maturity in the church. We would have to confront lovingly when we have a problem with a brother - but from what I've experienced - we would also have stronger relationships in the church or wherever we are having problems. May God bless us so that we begin to take this very wise advice and have stronger relationships in every aspect of life.