Its a lesson from Paul to the Christians at Corinth to stop identifying with, and choosing among various teachers to the exclusion of all others. Listen to the message, not the speaker.
As always you MUST observe and preserve contexts to avoid confusion. Now then, the chapter divisions of the books of the Bible are not present in the original Hebrew and Greek manuscripts. They were added much later for ease of study. So here, we need to back up to chapter 3 in order to set the context for chapter 4. Paul is addressing the Christians at Corinth.
In chap 3, Paul is stressing that it is unimportant which teacher we identify with
1Co 3:21 So don't boast about following a particular human leader. For everything belongs to you—
1Co 3:22 whether Paul or Apollos or Peter, or the world, or life and death, or the present and the future. Everything belongs to you,
1Co 3:23 and you belong to Christ, and Christ belongs to God.
He continues into chap 4
4 So look at Apollos and me as mere servants of Christ who have been put in charge of explaining God’s mysteries. 2 Now, a person who is put in charge as a manager must be faithful. 3 As for me, it matters very little how I might be evaluated by you or by any human authority. I don’t even trust my own judgment on this point. 4 My conscience is clear, but that doesn’t prove I’m right. It is the Lord himself who will examine me and decide.
5 So don’t make judgments about anyone ahead of time—before the Lord returns. For he will bring our darkest secrets to light and will reveal our private motives. Then God will give to each one whatever praise is due.
NOW HERE IS PAULS MAIN CONTENTION HERE >>>
6 Dear brothers and sisters,[a] I have used Apollos and myself to illustrate what I’ve been saying. If you pay attention to what I have quoted from the Scriptures,[b] you won’t be proud of one of your leaders at the expense of another. 7 For what gives you the right to make such a judgment? What do you have that God hasn’t given you? And if everything you have is from God, why boast as though it were not a gift?
See what he says about this in another place:
1Co 1:12 Some of you are saying, "I am a follower of Paul." Others are saying, "I follow Apollos," or "I follow Peter," or "I follow only Christ."
1Co 1:13 Has Christ been divided into factions? Was I, Paul, crucified for you? Were any of you baptized in the name of Paul? Of course not!
All the teachers and preachers he named taught Christ crucified. The same message. But their personalities and styles and deliveries were different. He was saying don't judge one of them at the expense of the others.
Still confused? Then please ask another question. Thats why we are here.