If you belong to the Latin Rite of the Catholic Church, you may find the idea of married priests strange. This is because the majority of priests within the Catholic Church belong to the Latin/Roman Catholic Church.
In the Eastern rites of the Catholic Church, it is commonly misunderstood that priests can get married.
Just like in the Latin Church, priests are not allowed to become married. However, married men are allowed to be ordained to the priesthood.
Therefore, it is typical to see married men in the seminary of the Eastern Rites piously preparing to become successors of the apostles and presbyters of God’s Holy Catholic Church.
Pope Benedict XIV piously stated in his encyclical ‘Allatae Sunt’ in 1755 the following:
“Another example is the freedom enjoyed by priests of the Oriental and Greek church to remain married to their wives after their ordination (see can. Aliter, dist. 31 and chap. Cum olim, de Clericis Conjugatis).
Considering that this practice was at variance neither with divine nor natural law, but only with Church discipline, the popes judged it right to tolerate this custom, which flourished among Greeks and Orientals, rather than to forbid it by their apostolic authority, to avoid giving them a pretext to abandon unity. So does Arcudius assess the matter.” (Concordia bk. 7, chap. 33)