The priesthood began with Jesus. During his three years of public preaching, he chose twelve men from the crowd, men to be his disciples, his students. At the time, they had no idea what they would ultimately learn, but they still gave up everything to follow Jesus. He spent those three years teaching the public, but also teaching His disciples, telling them things he did not reveal to the crowd. He was training them through this whole time. Eventually, his time on Earth drew close to the end. At this time, Jesus celebrated the Last Supper with the Twelve. He broke bread and wine, as was tradition for Jews, but the celebration was altered: He said to them, "This is my body ... This is my Blood ... Do this in memory of me." And with these words, the bread became His Body, the wine his blood. The next day, Jesus died. Three days later, he rose again. And he continued with his Disciples, preparing them for the times when He could not be with them in flesh. And He send the Holy Spirit down on them, that they would continue what he had left unfinished.
The Twelve Apostles were the original bishops and also the original priests. They broke bread in homes in the name of Jesus, and they ministered to the poor. However, their ministry attracted a great number of people. They could not do it all themselves. And so they ordained other men to be priests as well. These men also performed the Eucharist, the breaking of the bread, for "Eucharist is 'the source and summit of the Christian life.' 'The other sacraments, and indeed all ecclesiastical ministries and works of the apostolate, are bound up with the Eucharist and are oriented toward it'" (Catechism, III.I.1324).
Throughout the years, the Apostles and their successors, the bishops of the church, continued their work, and ordained more priests along the way. "In the early church, a lay person could advance" to any position within the Church without first becoming a lower order (EB, vol 6 pg 21). In this manner, a man could skip deaconhood or priesthood and immediately become a bishop or even pope, if he were so chosen. In addition to their vocation, these priests oftentimes had families of their own. And this lead to a few unwanted practices, such as priests leaving Church properties to their heirs. Meanwhile, another form of religious expression had emerged: the religious. These began as hermits and then monks. These religious often were more holy than their priest counterparts, and people started to go to see the monks and hermits for advice. The Church took note of this, and since these religious had vowed to live a celibate life, the Church thought that perhaps the priesthood could benefit from such a policy. So in the 4th century A.D., the Church began to enforce the policy of celibacy for priests, and by the 12th century, any man becoming a priest also took a vow of celibacy when he underwent Holy Orders. The priesthood continued to remain celibate within the Catholic Church for the next eight hundred years, and remains thus today.
In recent times, there have been many changes in thought concerning the Church and religion. The second Vatican Council spearheaded this change in thought. This council changed many aspects of the Church but also reaffirmed many. One change was the removal of the necessity of celibacy for deacons. The current "rules" for becoming a priest in the Catholic Church are to be a baptized male of the required age or older, have received a proper and adequate education, "are of suitable character, and have a specific clerical position awaiting him."
In the present day, numerous controversies regarding priesthood have come up. Among these are the belief that priests should not be made to remain celibate. The critics to celibate priests argue that celibacy only separates the priests more from the people they minister to. And to bolster their argument, the Bible does not say that priests must remain celibate. Again, this is a practice that began in the middle of the Church history. There is, therefore, no reason, that priests should remain celibate. The Eastern Orthodox Church, which is closely related to the Catholic Church, allows married priests. It is possible that in the future, parishioners will go to Mass on Sundays and the priest may have a family of his own.
Some argue that the Church should allow women to become priests. Unlike married male priests, this argument does not hold as much ground. Because while Jesus did chose married men among his Apostles, he did not choose women. There is also the fact that in Mass, the priest takes the place of Jesus in the ritual of the Last Supper, the Eucharist. Jesus was himself a man. For this reason, a woman cannot adequately represent Jesus. So while it is possible that non-celibate priests may be found in the future Roman Catholic Church, women priests will not be found there.
The priesthood as formed by Jesus has evolved over the years to it's present form, but has also remained mostly the same. Formed to minister to the people of the Church and to give them the sacraments, including Jesus in the Eucharist, the priesthood has grown into it's present state over the thousand of years. The priesthood will continue in the Church as long as the Church exists, until the end of time.
Catechism of the Catholic Church. Internet document. http://webzone1.co.uk/www/jcrawley/euch1.htm