This call to correct or restore the one caught in sin is in fulfillment of our responsibilities under Christ's law. This law can be encapsulated in the command to love. If I truly love my brother, when I see his soul in jeopardy I will seek to warn and correct him. James revealed the value of such correction while instructing brethren in this responsibility. There is value in correction for the simple reason that truth is better than error.
Righteousness is to be preferred over sin.
The teaching of error and the commission of sin can have dire consequences that are eternal in nature. We can see this through a simple illustration. Consider the teacher who instructs your children. An important part of her work is correcting papers. If she were to cease making corrections, accepting any answer no matter its validity, she would be doing a disservice to her students.