This is an interesting question to answer, as the Bible does not even teach that there are to be “priests” in the New Covenant established by Christ. Please read our articles on the “priesthood of believers” and “confession of sin to a priest” for more information. The Bible addresses the celibacy of church leaders, but not celibacy of priests.
In regards to celibacy of church leaders, in 1 Corinthians chapter 7, the apostle Paul teaches, “An unmarried man is concerned about the Lord’s affairs — how he can please the Lord. But a married man is concerned about the affairs of this world — how he can please his wife — and his interests are divided” (1 Corinthians 7:32-34). In some instances, celibacy has a positive impact on ministry. If a church leader is free from spousal and familial responsibilities, he can better focus on ministering to others. Jesus mentions some becoming “eunuchs” for the kingdom of God (Matthew 19:12). Celibacy is definitely allowed for church leaders, and to a certain degree, it is encouraged. However, Scripture nowhere requires celibacy for those serving in positions of church leadership.
In 1 Timothy 3:1-13 and Titus 1:6-9, the Apostle Paul seems to assume that elders, bishops, overseers, and deacons will be married. Notice the phrases “the husband of one wife” (1 Timothy 3:2, 12; Titus 1:6), “he must manage his own family well” (1 Timothy 3:4,12), and “his children obey him with proper respect” (1 Timothy 3:4; Titus 1:6). On a related issue, please read our article on whether these Scripture mean that a church leader must be married and have children. While these Scriptures are not a requirement for church leaders to be married, they most definitely present an allowance for church leaders to be married. It is therefore anti-biblical for any church to require celibacy of its leaders.
Why, then, does the Roman Catholic Church (and a few other Christian denominations) require celibacy of priests /church leaders? The celibacy of priests has an interesting history. The first official church statements requiring celibacy appeared at the Councils of Elvira (A.D. 306) and Carthage (A.D. 390), although clerical celibacy, to a lesser degree, definitely predated these councils. Ultimately, though, celibacy became the official requirement of the Roman Catholic Church due to the practice of nepotism. Church leaders were giving their children positions in the church, despite a lack of any qualifications or training. Further, church leaders were giving church property to their descendants. As a result, the Roman Catholic Church mandated celibacy in order to keep its priests from having familial attachments which made nepotism attractive.
Again, the Bible encourages, but does not demand celibacy of priests / church leaders. In fact, Paul recognizes that most church leaders will be married. The Roman Catholic requirement of celibacy is a sad example of the Church taking something that the Bible encourages and transforming it into a requirement in order to protect its own interests. Sadder still is the damage that has been done as a result of the Roman Catholic Church’s anti-biblical requirement. Men whom God has not gifted or called to be celibate (1 Corinthians 7:7) are being required to be celibate, and the result is tremendous failures in the areas of adultery, fornication, and the sexual abuse of children.