In 1 Corinthians 4:9 Paul contrasts his success with the success of the Corinthian church. He suggested that men like himself and Apollos were treated as if they had been sentenced to death, like they had become a spectacle or embarrassment to the church and to the world. Why? Because they preached that the foolishness of Christ was greater, stronger and smarter than the wisdom of the world. He preached that the wisdom of Christ was opposed to the wisdom of the world, opposed to the wisdom of worldly scholarship and philosophy.
It is important to note that Christianity is not opposed to scholarship and philosophy per se, but to scholarship and philosophy that tries to function apart from or independently of God and His Word. God is not opposed to intelligence. He created it. What He is opposed to is intelligence that suppresses the truth in unrighteousness, that tries to hide the fact that all people are responsible to God for their behavior and beliefs.
1 Corinthians 4:10 draws a stark contrast between worldly success and gospel faithfulness. "We are fools ... you are wise. We are weak ... you are strong. You are held in honor, but we in disrepute." The difference is not subtle, but stark. Paul and Apollos were poor, buffeted (beaten) and homeless. And they worked with their own hands, as did the lowest social strata in Greek society. They were everything that was despised by successful Greeks.
In 1 Corinthians 4:14 he tells the church that he has not written these things to shame them, but to warn or admonish them. A synonym for admonish is discourage. Paul was discouraging the saints in the use of worldly wisdom, which he also called foolishness. It is important to see that Paul engaged in discouragement as a method of teaching the gospel. Faithfulness involves not believing and not doing the wrong things as much as it does believing and doing the right things.
A father loves his family. A father has an obligation to care for his family, to teach them what is right and to point out what is wrong, to encourage them, but also to discipline and discourage them (from the wrong things). A father has authority, responsibility and accountability within the extended family structure. A father doesn't work for the benefit of his family in order to get paid. Being a father is not a job. A father works for his family without consideration for his own benefit. A father is there in good times and in bad times, to encourage and to discourage, to point out the truth and the lies.
Finally, said Paul, "be imitators of me" (1 Corinthians 4:16). Don't forget the context of this verse. Paul has been telling them about the differences between those who live according to the wisdom of the world -- which he also calls foolishness, and those who live according to the wisdom of God. He has essentially told the Corinthians that the success of their church has come from their commitment to worldly wisdom. He will continue to admonish the Corinthians throughout this letter, and the next, because of their worldliness and sin. They were engaged in worldly thinking and outright sin -- all in the name of Christianity! He told them that they were proud of the success that their church enjoyed -- it's wealth and political power -- because they were worldly minded and unfaithful to Christ. Their pride in their church was an expression of their faithlessness and their misunderstanding of the gospel.
In contrast to what they were believing and doing, Paul said, "be imitators of me" (1 Corinthians 4:16). He wanted them to imitate real faithfulness rather than to faithfully believe in imitation Christianity. Like Apollos before them, they were trying to incorporate what they knew about Jesus Christ into their Greek worldview. They succeeded in making Jesus fit comfortably into Greek society, and the church had grown drastically as a result.