Paul addresses the Corinthian's identity crisis. Though they are in the Spirit (saved), they require being spoken to as carnal, and as babes. They mind the wrong things and glory in the wrong things. They recognize that they are not under the law, yet fail to understand what grace teaches. Paul asks them again, "Know ye not?" This time calling out despicable behaviour that even the world identifies as wrong.
Not only did the Corinthians put up with the behavior, they gloried in it, allowing this false teaching to corrupt the assembly. Paul tells them to separate from the "old leaven" (wrong doctrine and behavior) that leavens the whole lump. This is so that they can be who they already are in Christ. Old things are passed away, they are a "new lump" (new creature).