Fearful Persuasion
2Cor 5:11 Since, then, we know what it is to fear the Lord, we try to persuade men. What we are is plain to God, and I hope it is also plain to your conscience.
As he said in the previous verse, we are all subject to judgement, and in particular concerning teachers. John writes, "There is no fear in love. But perfect love drives out fear, because fear has to do with punishment. The one who fears is not made perfect in love." 1John 4:18 Given that we are are imperfect, the fact of judgment invokes fear. This is one aspect of the fear of the Lord which motivates Paul. But another is the fact that Paul fears for the lost. He fears on behalf of those headed for hell fire. If you're not trying to persuade people for the kingdom, what would motivate you to do so?
Note also that Paul assumes that men are persuadable - that people are not puppets. People are not "totally depraved" such that they cannot be persuaded by reasoning with them. Of Paul himself it is recorded, "Every Sabbath he reasoned in the synagogue, trying to persuade Jews and Greeks." Acts 18:4 The gospel can persuade reasonable men. Note for example the end of Peter's first sermon, "With many other words he warned them; and he pleaded with them, "Save yourselves from this corrupt generation." Acts 2:40
There are "men who speak abusively against whatever they do not understand; and what things they do understand by instinct, like unreasoning animals— these are the very things that destroy them." Jude 1:10 Among them are many religious people. But the gospel was intended for those who are reasonable, who listen with sincerity, and who can be persuade by the truth.