What is often overlooked is 1 Tim 3:2 wherein Paul says "a bishop must be above reproach, the husband of one wife" (RSV). The early Church like the Jews of the time (and even the pagan Romans and Greeks) did not practice polygamy nor did the Church allow divorce. Why then the requirement that there be only one wife? It must mean that if widowed he had not remarried. The Church has never forbidden that (cf 1 Cor 7; 1 Tim 5) but also saw it as a sign of strong passions. The requirement that a candidate for the episcopacy is not subject to such passions would imply that it was a requirement for anyone in sacred orders (deacons and priests are likewise bound). How could he show this? By having raised his family at the time of ordination and not producing any more children or by being and remaining single. That's part of the conclusion of "The Apostolic Origins of Priestly Celibacy" by Christian Cochinin SJ and published by Ignatius Press (not all Jesuits are bad). There is plenty of evidence cited in that work that perfect continence was required of all clerics from the beginning of the Church. It seems that this changed for the Eastern Churches under the influence of heresy but they kept the requirement for the episcopate. I also recommend Stefan Heid's "Celibacy in the Early Church."