Paul faces criticism from another group doing ministry, because he doesn't carry the same "credentials" and "recommendations" that they do. Paul looks at the fruit of the gospel and says that's all the credentials I need.
Paul uses the analogy of familiar scene called a Roman Triumph, which includes a very familiar fragrance, and says that’s what disciples of Jesus are like – we are like a fragrance that to some people means life, and to others means death.
Paul has a situation in Corinth where a man had sinned against someone in the church. He lets them know the sin isn't just against him, but against everyone. He begged them to deal with the situation so the man could be restored. He also encouraged them to forgive him, so that Satan didn't get a foothold in the church.
Jesus made six statements in the gospels of Luke and John about discipleship: three from the negative, saying, if this or this is true you cannot be my disciple, and three from John in the positive, saying, this is how people will know you are my disciple. We put those six statements together to derive a working definition of a disciple of Jesus.