For we were the first to come all the way to you with the gospel of Christ.
2 Corinthians 10:14b
Paul is reminding the church at Corinth of the unique relationship he has with them. Paul and his team were the first Christians to bring the gospel to Corinth. They were the beach head storming advance wave of hard-fighting gospel preachers who shared the unique experience of seeing the first hard-won converts in the city. God used them to start the process of building the church there.
As is often the case with Paul, other believers continued where he had worked, because Paul kept moving on to new cities still in need of hearing the good news because his vision was to be a gospel pioneer. And occasionally false teachers would arrive after Paul's departure. In the case of the Corinthians, these false teachers claimed to be apostles and in order to build up their own prestige, they bad-mouthed the ministry of Paul, forcing him to defend his ministry to the church God had led him to start. It had to be painful for Paul to do this.
As difficult as it was to be defending himself to his own children in the faith, Paul does so humbly and with the gospel at the center of the discussion. He subtly points out that false teachers don't focus on the gospel. He appeals for the Corinthian church to remember the gospel and remember the clear, simple focus of Paul's ministry. This should have brought the Corinthians back to the most important thing... the gospel of Jesus Christ!