Who was the man living with his father's wife in the Corinthian church?
The supplied passage does not provide a personal name; it identifies the offender as a stepson living with his stepmother as husband and wife. The Corinthian congregation knew of the gross immorality yet remained puffed up instead of mourning and removing him from fellowship.
Les explains that commentators are largely agreed the offender was likely a stepson who was living with his stepmother as husband and wife. This was gross immorality, even for Corinth. The real point of condemnation from Paul was that the Corinthians were puffed up and had not mourned, so that the one who did this deed might be taken away from among them—removed from church fellowship, not put to death. All the groups, whether following Peter, Apollos, or Paul, knew about it and were not bothered. It brought reproach upon the name of Christ throughout Corinth because even the pagans knew what was going on.
It is reported commonly that there is fornication among you, and such fornication as is not so much as named among the Gentiles, that one should have his father’s wife.