Not a big deal, but to set the record straight, the verse you mentioned is in I Cor. 5, not chapter 6.
In this verse, Paul is not attempting to deal with what to do with false teachers. He does that elsewhere and in numerous places:
Romans 16:17 Now I beseech you, brethren, mark them which cause divisions and offences contrary to the doctrine which ye have learned; and avoid them. 18 For they that are such serve not our Lord Jesus Christ, but their own belly; and by good words and fair speeches deceive the hearts of the simple.
Titus 3: 9 But avoid foolish questions, and genealogies, and contentions, and strivings about the law; for they are unprofitable and vain. 10 A man that is an heretick after the first and second admonition reject; 11 Knowing that he that is such is subverted, and sinneth, being condemned of himself.
II Tim. 3:5 Having a form of godliness, but denying the power thereof: from such turn away. 6 For of this sort are they which creep into houses, and lead captive silly women laden with sins, led away with divers lusts, 7 Ever learning, and never able to come to the knowledge of the truth. 8 Now as Jannes and Jambres withstood Moses, so do these also resist the truth: men of corrupt minds, reprobate concerning the faith
As did John:
I John 2:9 Whosoever transgresseth, and abideth not in the doctrine of Christ, hath not God. He that abideth in the doctrine of Christ, he hath both the Father and the Son. 10 If there come any unto you, and bring not this doctrine, receive him not into your house, neither bid him God speed: 11 For he that biddeth him God speed is partaker of his evil deeds.