Non-Catholic Christianity is like a shattered mirror; it reflects something that precedes it, but it might not reflect parts of the object at all. The image that is seen in the mirror is similar to the object, and those similarities are good, but it is not the full image of the object, and it certainly is not the actual object itself.
The Protestant Church of Christ partially understands spiritual fatherhood, and it utilizes a different vocabulary than that of the Catholic Church of Christ—words that are, in its estimation, more biblically tolerable than the Catholic Church’s use of the respectful address of “father” for her priests. Instead, some portions of the Protestant Churches of Christ use the word “discipler” (which means “teacher”), some use the word “mentor” (which means “teacher”), some use the words “brother” or “sister”, and some use no title or address at all to refer to any fellow believer who helps them on their journey. But the roles are similar: spiritual mentorship, spiritual fatherhood.
Your communities exercise the role of spiritual fatherhood primarily by engaging in Bible studies, preaching, and building accountable relationships. These are good things. The Catholic understanding of spiritual fatherhood, however, because it is not a shattered reflection, but the fullness of Christianity, is much clearer; spiritual fatherhood is catechetical, sacramental, and pastoral.
A priest is not a father in a divine sense; he is a father in a spiritual and pastoral sense. A priest is not God; God entrusts the priest with the spiritual welfare of his flock, and a priest exercises his spiritual fatherhood in several ways. The first way, usually, is at a child’s Baptism. Like a biological father who witnesses his child’s birth, a priest baptizes the child, and the child is born again (John 3:3).1
A priest is a spiritual father when he hears confessions. When a Catholic confesses sin to a priest, he addresses the priest by saying, “Forgive me father, for I have sinned.” Catholics do not believe the priest is God the Father; they address him as a spiritual father—a man, and that is why the priest refers to any person who comes to Confession as, “my child.” At Confession, the priest looks upon the repentant sinner with compassion and mercy—as a father.
A priest is a spiritual father when he opens God’s word and teaches people not what they want to hear, but what they need to hear.
A priest is a spiritual father when he celebrates the Mass, as he stands in persona Christi, when he nourishes Christians with the Bread of Heaven.
A priest is a spiritual father when he witnesses a Marriage (the bride and bridegroom “perform” the wedding), and when he blesses the new “one flesh” and looks forward to the lives that the Marriage will bring into the world.
A priest is a spiritual father when he anoints the sick to either bring them back to health or prepare them for their new life (cf. Mark 6:13, James 5:14-15).
A priest guides, protects, and disciplines all that are under his watch. He stands up for the defenseless, for life, the poor, the marginalized, the ill, and the elderly. The priest’s family is not a wife and biological children; he is married to the Church, and his flock is his family—he is its father.
1 In the case of adult conversion, the priest will baptize the convert if she has not already been baptized.