The Church Fathers are those wise and learned men from the first, second, and third generation of the Catholic Church that spoke about, defended, and made commentary on the teachings of the Catholic Church. Because they were the disciples of the Apostles, whom are the Church’s first bishops, and the discipeles of the disciples of the Aposltes, following the first fathers as good sons, and the disciples of the disciples of the disciples of the Apostles, following the good sons just as they followed the first fathers, they are the best source of information on the infant Church and on her history. Although some of them did make mistakes - being only human - their writings are not without credibility, wisdom, and truth. We call these men “Fathers” for three reasons:
First, they are bishops. Bishop means “father”. The bishop is to a particular church an image of God the Father, just as the Son, in whose Person the bishop acts, is the Image of the Father. He teaches, governs, and sanctifies the church in love and mercy, and he is to be honored just as Jesus Chritst honors the Father. Because the Catholic Church is the Body of Christ, and the bishop, who is a member of this Body, is a vicar of Christ for the particular church, and each particular church is the Catholic Church, the Church is in the bishop, and so, whoever dishonors the bishop dishonors the Church. Hence, the Church Fathers ought to be given great honor, and especially since they are now among the immortal. Moreover, the Fathers succeeded the Apostles in the office of the bishop, just as a son succeeds his father in his line of work, just as Christ was a carpenter after His foster-father and a Son after His Father. So the Church Fathers are to especially be revered as the fathers of the Catholic Church.
Second, they are teachers. This goes along with the office of the bishop. The Church is our Holy Mother and Teacher, and in as far as she is in the bishop, he is the father and teacher of his particular church. This is in light of the Blessed Eucharist, God Himself, who, as Love Itself, is not just the bond of unity among Christians but is Unity Itself, for Love is Unity Itself, and, God is both One and Unity, being a simple God; this Blessed Sacrament unites the Church and the bishop even greater than sex unites a man and a woman in holy matrimony, for the marriage between the Church and the bishop is more powerful, deeper, and greater than any physical and spiritual intimacy can ever hope to be. Because the Church Fathers are teachers, they are rightly called “Fathers”, for in the time of Christ, a teacher was as a father to his pupils and the pupils as sons to the teacher, and this is true of the Fathers. But what did the Church Fathers teach? They taught the Apostolic Tradition, the Sacred Tradition, the Living Tradition, by not only their writings and words but also their lives and works, for this Tradition is a living transmission of the Word of God, just as the husband ejaculating sperm into the wife is a living transmission of the baby.
Third, they are spiritual fathers. I say “spiritual fathers” because they are chaste yet have many sons and daughters: those who belong to their flock and those whom they win for Jesus Christ by their prayers and penance. They are “spiritual fathers” because they are to the particular church what a shepherd is to his sheep - indeed, many who own a pet like to pretend the pet is their child and they its parent, but what the owners pretend is true, is truly real for the bishop and his church - and because they acted as fatherly figures for the Christians: guiding, guarding, correcting, and giving good examples to them. They are also “spiritual fathers” because they, in light of their writings, laid down the foundations of the Catholic Faith: not that they created it, for the Fath is from God through His Church, just as Christ is from God through Mary, but that they, because faith is from God through His Church, helped to expound upon, teach, and pass on the living Faith.