For those unfamiliar with the biblical concept of identifying "fatherhood" with "priesthood" please first take a look at a post I wrote entitled "Calling Priests Father" as it examines the words of Saint Paul: "I became your father through the Gospel" (1 Cor 4:14-17). Let's take a look at Church History. In the early Church, clerics did not generally bear standard titles. It seems that "pappa" (Greek for "daddy") was an accepted form of address for bishops in general. In the West, "pappa" or the Latinized form "papa" became almost exclusively associated with the Bishop of Rome since the time of Leo the Great (A.D. 440-461). A notable exception is the Coptic Patriarch of Alexandria who bears the title "Papa" or "Pope". In the late medieval era, clergy bore titles of respectability. If you've read Eamon Duffy's Stripping of the Altars, you will have observed that priests prior to the Reformation were simply "Sir" which is the English version of the Latin "senior" meaning "older" a rather fitting title for one who is a "presbyter" meaning "elder" in Greek. One also finds "Dom" or "Don" as a title of address from the Latin "Dominus" or "Master" (especially in Italy). Benedictine monks on the continent retain the title of "Dom". Those who like champagne will remember "Dom Perignon" the Benedictine inventor of the bubbly. Prior to the 1800s, priests belonging to religious orders were almost universally "Father, Pere, Padre, etc. The Benedictines however retained "Dom." In the new world, Spanish speakers frequently referred to priests as "Padre" since the establishment of Catholicism in Latin America was laid by Franciscan, Dominican, and Jesuit missionaries, all who would have been religious "Padres." In England, secular Catholic priests (priests not belonging to an order) were simply addressed as "Sir", "Mister", or "Doctor" (if he possessed a doctorate). This was the case for both Anglican and Catholic clergy. It seems that the title "Father" emerged as a universal English title of address among Catholics with the reestablishment of the Catholic hierarchy in England so that Catholic priests would be distinguished from Anglican priests. As an aside, Catholic priests in England were not allowed to wear the cassock publicly in England (this right being reserved to Anglican clergy), and this oddity gave rise to the Anglo-American custom of the Catholic priest wearing the black suit instead of the black cassock in the streets. Ironically, wearing of the cassock in public in England was a symbol of Protestantism!
