Jamieson, Fausset and Brown on 1 Corinthians 5:2

2. puffed up--with your own wisdom and knowledge, and the eloquence of your favorite teachers: at a time when ye ought to be "mourning" at the scandal caused to religion by the incest. Paul mourned because they did not mourn (2Co 2:4). We ought to mourn over the transgressions of others, and repent of our own (2Co 12:21) [Bengel].

that--ye have not felt such mourning as would lead to the result that, &c.

taken away from among you--by excommunication. The incestuous person was hereby brought to bitter repentance, in the interval between the sending of the first and second Epistles (2Co 2:5-10). Excommunication in the Christian Church corresponded to that in the Jewish synagogue, in there being a lighter and heavier form: the latter an utter separation from church fellowship and the Lord's house, the former exclusion from the Lord's Supper only but not from the Church.