Many Protestants point to the "doctrine of demons" passage in scripture where it talks about people forbidding to marry as proof against priestly celibacy. What they fail to understand, though, is that celibacy is a discipline, a practice, not a dogma. The Eastern rites allow married priests (though they must be married at the time they are ordained, they can't get married after they are ordained.) And there are even some rare cases of Latin rite priests being married, for instance if an Anglican priest who is married converts and wants to remain a priest, if they get permission they would be a married priest.
Eastern Catholic priests do not have to make a vow of celibacy, and no one is putting a gun to anyone's head forcing them to become a Catholic priest in the Western rite. Nobody is forbidding marriage, marriage is a wonderful sacrament, and brings many blessings. Catholics think marriage is a very good thing...but they also believe living a celibate life by choice is also a very good thing (like Paul says.) A priest's job is a 24/7 job, they are called at all hours of the night and day, they say several masses a day, and when they're not doing that they are praying. It's a very busy life, and so it's common sense that so that they are not divided between wordly things (like having a wife and kids) and spiritual things (like their flock), it's a good idea to remain single so that they can devote their entire life to God alone. No, it's not a dogma, but it is a discipline of the Western Rite.
"But look at the sex abuse scandal, isn't that proof that it's not 'natural'?"
The media loves to push this idea. However, it's just plain wrong. There are just as many, if not more scandals in non-Catholic churches among non-Catholic clergy as there are among Catholic clergy. The media just loves to point out Catholic clergy more than others to prove their point that "to go without sex is unnatural and bad." The problem is not unmarried priests, it's a culture of sexual depravity, as evidenced by the amount of sexual scandal everywhere in every church and outside of church. On top of that, it's not just sex that the abuse involves, it is disordered sex. If it were just a matter of satisfying a normal desire, most of the abuse victims would have been female. As it stands, that is not the case.
This, I think, explains things well:
If a priest-or any person for that matter-has a disordered sexual desire, marriage is not the cure. Experiencing the redemptive power of Christ in one's fallen sexuality is the cure. Getting married will only involve the transferal of a man's unhealthy lust to his wife or children. Conversely, if a man abuses his wife, the solution to the problem is not the renunciation of his call to marriage. The solution lies precisely in his call to marriage-to love his bride as Christ loved the Church.
The fact that marriage is not the solution to pedophilia can be demonstrated by looking at the statistics. Per capita, Catholic priests do not have a higher incidence of pedophilia than do married clergymen. The reason why you don't hear as much about the other cases is because of the anti-Catholic bias that permeates the media.
Here is an article that examines the amount of abuse in the Catholic church compared to the rest of the world. Admittedly, it is from a Catholic source, but it does use resources that are not Catholic to support its claims.
Too often, assumptions have been made that this problem is worse in the Catholic clergy than in other sectors of society. This report does not support this conclusion. Indeed, it shows that family members are the most likely to sexually molest a child. It also shows that the incidence of the sexual abuse of a minor is slightly higher among the Protestant clergy than among the Catholic clergy, and that it is significantly higher among public school teachers than among ministers and priests.
Even this site, which is not Catholic at all, admits there is no proof that it is any worse among Catholic clergy than anywhere else:
So, it's a bit of a red herring that is often claimed as proven fact. Even if one takes the highest amount of alleged abuse among clergy, it's not more than 50%, it's not more than 25%, it's not more than 10%...it's around 3%. And remember, those are the HIGHEST amounts. So most priests, just like most people, do not engage in such vile behavior. And those who do certainly need to be removed and punished.