The tradition of single priests is Canon law, not a dogma, which means it is not set in stone, and could change. The married priesthood is not unbiblical per se (i.e., Peter was married), but there is much scriptural and historical evidence supporting celibate priests.
The Church Fathers of the first four centuries consistently spoke against the married priesthood. St. Epiphanius speaks of the accepted ecclesiastical rule of the priesthood (kanona tes ierosynes) as something established by the Apostles. (Haer., xlviii, 9) “Holy Church”, he says, “respects the dignity of the priesthood to such a point that she [the Church] does not admit to the diaconate, the priesthood, or the episcopate, nor even to the subdiaconate, anyone still living in marriage and begetting children.” (Haer., lix, 4).
The writings of the Church fathers show that, in the early Church, married priests were not the accepted norm in the main centers of Alexandria, Antioch and Rome. They considered it a “problem” that existed in the outlying regions. By the 3rd century there were almost no married priests and several councils put the issue to rest until around the 9th century when many bishops and priests took wives and had children. The state of the priesthood fell to an all time low. A huge problem emerged with priests “willing” Church property to their families. Up to that point, the principle of celibacy was never completely surrendered in the official enactments of the Church. In 1123, celibacy was made official. Although, throughout history there have been scattered instances of abuses of the Canon Law, the Roman Catholic Church has consistently stuck to this position on celibate priests.
Nevertheless, there are married priests. Most married Catholic priests are part of the Eastern Catholic Churches, also known as the Eastern Rite. But there are about 70 Catholic priests in America who are married.
How could this happen? Theses men got married while serving as priests in other Christian denominations, usually the Anglican or Lutheran churches. If such a priest decides that he would be better off within Catholicism, he can apply to a local bishop who then submits a special application to the pope, with decisions being made on a case-by-case basis. A special provision instituted in 1980 by Pope John Paul II allows the ordination of married men in certain cases.
Priests who marry can not advance up to a rank of Bishop.
Recently there are two stories of newly ordained married men, click the links below to see their stories: