Protestants take the priestly celibacy as unbiblical or unnatural.
They claim that every man must obey the biblical injunction to "be fruitful and multiply"(Gen. 1:28) and Paul command that "each man should have his own wife and each woman her own husband"(1Cor. 7:2). They also argue that celibacy somehow causes illicit sexual behaviour or perversion or at least correlates with higher incidence of it.
Although most people are at some point of their lives called to the married state, the vocation of celibacy is explicitly advocated as well as practiced by both Jesus and Paul. Paul actually endorses celibacy for those capable of it. (1Cor. 7:8-9).He specifically clarifies:
1 Cor. 7:6-7 I say this as a concession, not as a command. I wish that everyone was as I am. But each has his own gift from God, one this way, another that.
Paul prefers celibacy in 1 Cor.7:27-34) and
1 Cor. 7:38 So then, the one who marries his own virgin does well, but the one who does not, does better.
After Jesus teaching in Mat. 19 on divorce and remarriage, the disciples exclaimed, "If such is the case of a man with his wife, it is not expedient to marry (Matt. 19:10). This remarks prompted Jesus' teaching on the values of celibacy "for the sake of the kingdom"(Matt. 19:11-12).
Protestant reject celibacy considering it as a dogma or a doctrine of Catholic Church and maintain that priestly celibacy was made mandatory much later in the Church history:
It is taken by protestant as a central and irreformable part of Catholic faith, believed by Catholic to be coming from Jesus and the apostles and their objection is that, since Peter was married (Mark 1:30) there cannot be basis for this in Bible.
In reality the celibacy is not the rule for all Catholic priest even today. In Eastern rite Catholics, married priest are the norm, just as they are for Orthodox and Oriental Christians. In Eastern churches married men may become priests, unmarried priest may not marry, and married priests, if widowed, may not remarry. In western or Latin-rite Church the tradition has been for priests as well as bishops to take vows of celibacy, a rule that has been firmly in place since the early Middle Ages, with exception to those who are married priests in Latin-rite, who are converts from Lutheranism and Episcopalians. So all these variation in Catholic church indicates that priestly celibacy is not an unchangeable dogma but a disciplinary rule. Just as the Peter was married so also any of the nearest pastor of Maronite Catholic Church and both are not contrary to what Catholic faith teaches.
Protestants argue that only a man who has demonstrably looked after a family is fit to care for God's Church and an unmarried man is somehow untried or unproven. This is what Paul taught in 1 Tim. 3:2, 4-5.
This is a literal interpretation of the scripture which leads to further absurdities. With the next verse it implies that only those who have children can become bishops. Further to this it implies that only those who can keep their children submissive and respectful in every way can become bishops and so on.
This literal interpretation creates another contradiction. Paul himself was eminent Church leader, was single and happy to be so. Unless Paul was hypocrite he could have hardly imposed a requirement on bishops that he did not himself meet. The point of Paul's requirement that a bishop be "the husband of one wife" is not that he must have one wife, but that he must have ONLY one wife. Conversely, Paul is saying that a bishop must not have unruly or undisciplined children(not that he must have children who are well behaved), and must not be married more than once(not that he must be married).
Lastly Protestants argue that by requiring at least some of its clerics not to marry, the Catholic Church falls under Pauls condemnation in 1 Tim.4:3 against apostate who "forbid marriage".
1 Tim.4:3 They will prohibit marriage and require abstinence from foods that God created to be received with thanksgiving by those who believe and know the truth.
In fact Catholic church forbids no one to marry. No one requires to take a vow of celibacy and those who do so take it voluntarily. They renounce marriage (Matt.19:12); no one forbids it to them. Any Catholic who doesn't wish to take such a vow doesn't have to, and he is always free to marry with Church's blessing. The Church simply elects candidates for the priest hood from among those who voluntarily renounce marriage.
Paul was actually referring to Gnostic sects through the ages that denounced marriage, sex and body as intrinsically evil. Some early heretics fit this description as did the medieval Albigensians and Catharists.
Celibacy is an eschatological sign to the Church, a living-out in the present of the universal celibacy of heaven: "For in the resurrection they neither marry nor are given in marriage, but are like angles in heaven"(Matt. 22:30)