Why did Paul write 2 Corinthians?
Paul wrote 2 Corinthians as a follow-up to his first letter. He defended his apostleship and encouraged the Corinthian believers, who had seemingly corrected the problems he addressed. Since his first letter accomplished its work and they dealt with the immoral person, he wrote rather than visiting personally.
Les explains that 2 Corinthians is a follow-up to 1 Corinthians, where Paul had to deal with many problems in the Corinthian church, which had problems like no other congregation under his apostleship. He had to get rather hard with them in 1 Corinthians, but in 2 Corinthians he comes back in defense of his apostleship and to encourage those who had seemingly corrected their problems. Les notes Paul had intended to go to Corinth personally, but the message came that his first letter had accomplished its work. They had dealt with the person involved in gross immorality, and he was evidently back in fellowship. So instead of going and coming down on them, he wrote.