I am hopeful this will help you in understanding when and why this practice exists.
Since the earliest times of our Church, we have used the title “Father” for religious leaders.
Bishops, who are the shepherds of the local Church community and the authentic teachers of the faith, were given the title “Father.” Actually, until about the year 400, a bishop was called “papa” for Father; this title was then restricted solely to addressing the Bishop of Rome, the successor of St. Peter, and in English was rendered “pope.”
ewtn.com/library/ANSWERS/WHYFATHR.htm
Perhaps the most pointed New Testament reference to the theology of the spiritual fatherhood of priests is Paul’s statement, “I do not write this to make you ashamed, but to admonish you as my beloved children. For though you have countless guides in Christ, you do not have many fathers.
For I became your father in Christ Jesus through the gospel” (1 Cor. 4:14–15).
Peter followed the same custom, referring to Mark as his son: “She who is at Babylon, who is likewise chosen, sends you greetings; and so does my son Mark” (1 Pet. 5:13). The apostles sometimes referred to entire churches under their care as their children. Paul writes, “Here for the third time I am ready to come to you. And I will not be a burden, for I seek not what is yours but you; for children ought not to lay up for their parents, but parents for their children” (2 Cor. 12:14); and, “My little children, with whom I am again in travail until Christ be formed in you!” (Gal. 4:19).
John said, “My little children, I am writing this to you so that you may not sin; but if any one does sin, we have an advocate with the Father, Jesus Christ the righteous” (1 John 2:1); “No greater joy can I have than this, to hear that my children follow the truth” (3 John 4). In fact, John also addresses men in his congregations as “fathers” (1 John 2:13–14).
By referring to these people as their spiritual sons and spiritual children, Peter, Paul, and John imply their own roles as spiritual fathers. Since the Bible frequently speaks of this spiritual fatherhood, we Catholics acknowledge it and follow the custom of the apostles by calling priests “father.” Failure to acknowledge this is a failure to recognize and honor a great gift God has bestowed on the Church: the spiritual fatherhood of the priesthood.
Catholics know that as members of a parish, they have been committed to a priest’s spiritual care, thus they have great filial affection for priests and call them “father.” Priests, in turn, follow the apostles’ biblical example by referring to members of their flock as “my son” or “my child” (cf. Gal. 4:19; 1 Tim. 1:18; 2 Tim. 2:1; Philem. 10; 1 Pet. 5:13; 1 John 2:1; 3 John 4).
catholic.com/library/Call_No_Man_Father.asp