Paul writes, “For though ye have ten thousand teachers in Christ, yet have ye not many fathers: for in Christ Jesus I have begotten you through the gospel” (1 Cor. 4:15).
The word translated “teachers” comes from the Greek noun pais, translated “child” and the verb agoo, translated “to lead.” We get English words “pedagogue” and “pedagogy” from this Greek word, paidagoogous. It seems that Paul considered the saints at Corinth as babes or children (cf. 3:1-3) but that he is simply referring to them as child-like spiritually is doubtful.  According to our verse, he gave birth to them through the gospel.  Paul is implying a relationship with them as a father in the same way he refers to Timothy as his son (1 Tim. 1:2). Though Corinth had many teachers, they only had only one spiritual father.  Giving birth to them through the gospel implies that their birth was as a result of Paul’s teaching because he was the first to introduce the gospel to them. He wrote that he gave birth (Aorist tense) referring to a particular time in the past.
The idea of being their father, Paul wanted them to follow his example and to be followers of him as he was of Christ (1 Cor. 11:1; 4:16). Certainly, that desire would be true whether he had this relationship, or not. But, the fact that he did share this attachment to them, he is hoping that they would have the same longing and share the same closeness due to his work among them. They didn’t share the same attitude toward him as he did toward them.