Why did Paul write 2 Corinthians after 1 Corinthians?
Paul wrote it as a follow-up to his first letter. Since the Corinthians had addressed the problems, including the gross immorality case, he wrote to defend his apostleship and encourage them, instead of visiting personally after learning the first letter accomplished its work.
Les explains that II Corinthians is a follow-up to I Corinthians. In the first letter Paul had to deal with many problems in the Corinthian church—problems unlike any other congregation under his apostleship—so he had to be rather hard with them. In the second letter he comes back in defense of his apostleship and to encourage those who had seemingly corrected their problems. 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.