The first six chapters of 1 Corinthians deal with problems from within the church. Problems affect all growing churches.
Yeast is used a a simile: immorality will alter the image of the church, making it unrecognisable and damaging the credibility of the gospel.
Yeast is often used to demonstrate the presence of evil, e.g. the incorrect teachings of the Pharisees
False teaching and immorality distort the teaching of the gospel.
2 Corinthians chapter 7 indicates that the Corinthians, and the individual, repented
The Gospel: forgiveness, peace of mind, and freedom.