Why did the Corinthian church's sin bring reproach on Christ?
The Corinthian church's sin brought reproach on Christ because the congregation tolerated gross immorality within its midst, and the matter was public knowledge. Even the pagan city of Corinth knew what was happening, and the unjudged sin was not hidden, so the name of Christ was dishonored throughout the city.
Les explains that the situation involved gross immorality in the local Corinthian church—commentators pretty much agree it was a stepson and his stepmother living together as husband and wife. This was gross even for Corinth. Paul's real point of condemnation was that the Corinthians were puffed up instead of mourning, so that the offender might be removed from the congregation—not put to death, but removed from fellowship. All the factions, whether following Peter, Apollos, or Paul, knew about it and were not bothered. Les says you would have thought at least one segment would have demanded action. Because even the pagans knew and it was not hidden, the sin brought reproach upon the name of Christ throughout Corinth.