Paul followed in Jesus footsteps in his use of fictive family to convey theological truths but Paul also used fictive family metaphors to indicate his own sense of fond relationship for those he had nurtured in the faith:
1 Thessalonians 2:5-12
5 As you know and as God is our witness, we never came with words of flattery or with a pretext for greed; 6 nor did we seek praise from mortals, whether from you or from others, 7 though we might have made demands as apostles of Christ. But we were gentle among you, like a nurse tenderly caring for her own children. 8 So deeply do we care for you that we are determined to share with you not only the gospel of God but also our own selves, because you have become very dear to us.
9 You remember our labor and toil, brothers and sisters; we worked night and day, so that we might not burden any of you while we proclaimed to you the gospel of God. 10 You are witnesses, and God also, how pure, upright, and blameless our conduct was toward you believers. 11 As you know, we dealt with each one of you like a father with his children, 12 urging and encouraging you and pleading that you lead a life worthy of God, who calls you into his own kingdom and glory.
The author of 1 John is another author who uses the family metaphor in this way. He repeatedly refers to his readers as “children” or “dear children.”
Then there are these two examples where Paul casts himself as a father or mother, caring for troubled churches:
1 Corinthians 4:14-21
I am not writing this to make you ashamed, but to admonish you as my beloved children. 15 For though you might have ten thousand guardians in Christ, you do not have many fathers. Indeed, in Christ Jesus I became your father through the gospel. 16 I appeal to you, then, be imitators of me. 17 For this reason I sent you Timothy, who is my beloved and faithful child in the Lord, to remind you of my ways in Christ Jesus, as I teach them everywhere in every church. 18 But some of you, thinking that I am not coming to you, have become arrogant. 19 But I will come to you soon, if the Lord wills, and I will find out not the talk of these arrogant people but their power. 20 For the kingdom of God depends not on talk but on power. 21 What would you prefer? Am I to come to you with a stick, or with love in a spirit of gentleness? (Note: "Stick" in verse 21 could also be "rod," and would symbolize an instrument that a father would use to discipline a child.)
19 My little children, for whom I am again in the pain of childbirth until Christ is formed in you, 20 I wish I were present with you now and could change my tone, for I am perplexed about you.
But Paul also used a father to child metaphor to signify his fondness for particular individuals. In appealing to Philemon concerning Onesimus, Paul writes:
8For this reason, though I am bold enough in Christ to command you to do your duty, 9 yet I would rather appeal to you on the basis of love -- and I, Paul, do this as an old man, and now also as a prisoner of Christ Jesus. 10 I am appealing to you for my child, Onesimus, whose father I have become during my imprisonment. 11 Formerly he was useless to you, but now he is indeed useful both to you and to me.
With regard to Timothy, Paul writes:
But Timothy's worth you know, how like a son with a father he has served with me in the work of the gospel.
In the two letters to Timothy, letters where Paul’s authorship is considered less likely, we see Timothy referred to as a son as well (1 Timothy 1:2, 1:18, 2 Timothy 1:2, 2:1). Titus is also referred to “my true son in our common faith."
At first, this might seem an interesting side note to Paul’s use of the fictive family metaphor. However, church leader as father, based particularly the 1 Corinthians 4 passage, began to take on a life of its own. There is no evidence of a single leader authority structure in the New Testament churches, much less one who could be called “father.” But as Joseph Hellerman points out in The Ancient Church as Family, the idea of an earthly human “father,” as paterfamilias of the congregation, began to appear in the early second century in the writings of Ignatius of Antioch. (144) This in spite of Jesus teaching in Matthew 23:8-12
8 But you are not to be called rabbi, for you have one teacher, and you are all students. 9 And call no one your father on earth, for you have one Father -- the one in heaven. 10 Nor are you to be called instructors, for you have one instructor, the Messiah. 11 The greatest among you will be your servant. 12 All who exalt themselves will be humbled, and all who humble themselves will be exalted.
Caesar had used the household metaphor casting himself as the paterfamilias of the Empire. Jesus, Paul, and other New Testament writers envisioned a Church where all were brothers and sisters and God was the paterfamilias of the household, making all members siblings and equal to each other in status. Early church fathers, struggling to maintain order in congregations, innovated into a single leader model where they cast a singular leader of the congregation as the paterfamilias of the household. While Paul certainly used the “father and child” image to typify quality of his emotional relationship with churches and individuals, it seems highly doubtful that Paul envisioned the innovation that the early church fathers made of instituting a father authority figure. It thoroughly undercuts the specific teaching of Jesus in Matthew 23, and undercuts the general idea of undifferentiated status among believers, which is one of the essential reasons for the persistent “brother and sister” language. Furthermore, as the idea of a singular congregational leader became more thoroughly enmeshed with the idea of paterfamilias, it had to have had an impact on the likelihood of seeing women as fit for the role of congregational leader.