Not every Christian who wrote in antiquity is considered a Church Father. Theologians have settled on four criteria that must be fulfilled:
1. sound doctrine;
2. holiness of life;
3. Church approval; and
Those ancient Christians who don’t meet all these criteria are often described as “ecclesiastical writers” rather than Church Fathers.
Still, there is no official list of the Fathers, no process of canonization similar to a cause for sainthood. The ancient list attributed to Pope Gelasius is of uncertain origin; and, in any event, it was drawn up while the age of the Fathers was still in progress, so it misses some important later figures.
Some scholars say that Tertullian, Origen, and Eusebius should be called “ecclesiastical writers” rather than Fathers. Tertullian veered off into the Montanist heresy late in life. Origen seems to have experimented with several weird theological notions. Eusebius was a bit too cozy with the most notorious heretics of the fourth century, the Arians.
Yet recent reconsiderations have been kind to those three men. The Catechism of the Catholic Church cites Tertullian explicitly as a Father of the Church (n. 1446) and nine times invokes Origen as an authority. A French scholar summed up the matter: “the valuable services that these men have rendered to the Church” make them “exceptions.”
Some early authors would use the word “Father” only to describe a bishop, but eventually the term was extended to priests (like Jerome) and laymen (like Justin).