The real question is why a priesthood at all seeing that there is NO PROVISION for a priesthood in the NT church ..Christ is the final priest..
Greg Dues has written Catholic Customs & Traditions, a popular guide (New London: Twenty Third Publications, 2007). On page 166 he states, "Priesthood as we know it in the Catholic church was unheard of during the first generation of Christianity, because at that time priesthood was still associated with animal sacrifices in both the Jewish and pagan religions."
"A clearly defined local leadership in the form of elders, or presbyteroi, became still more important when the original apostles and disciples of Jesus died. The chief elder in each community was often called the episkopos (Greek, 'overseer'). In English this came to be translated as 'bishop' (Latin, episcopus). Ordinarily he presided over the community's Eucharistic assembly."
"When the Eucharist came to be regarded as a sacrifice, the role of the bishop took on a priestly dimension. By the third century bishops were considered priests. Presbyters or elders sometimes substituted for the bishop at the Eucharist. By the end of the third century people all over were using the title 'priest' (hierus in Greek and sacerdos in Latin) for whoever presided at the Eucharist."