Why do people sometimes provoke opposition to the gospel?
According to the context, people sometimes provoke opposition to the gospel because they become so obnoxious, seemingly for the sake of the gospel, that they instigate that kind of opposition. Paul warns against implying that suffering like his is necessary to prove belief, clarifying he does not write to shame but as beloved sons.
Les explains that these things happen where people become so obnoxious, seemingly for the sake of the gospel, that they instigate opposition. He notes Paul is warning the Corinthians not to think that if they have not suffered like he has, they are not believers. Paul writes not to shame them but as beloved sons, just as he called Timothy his son in the faith. Les points out Paul brought them the gospel that saved them from paganism and idolatry. In verse 15, Paul says though they have 10,000 instructors in Christ, they have not many fathers. Les sees this as meaning you can have many Sunday school teachers, pastors, or television evangelists, but only one or two really impact you to salvation. That is what Paul is driving at.