Over the past years, when a larger report of sexual abuse perpetrated by priests comes out, again and again opponents of priestly celibacy come out suggesting that the Church's discipline, in the Roman Rite, of requiring permanent and perpetual celibacy of its priests, contributes to the abuse crisis, or is even a major risk factor, or still more strongly, "will predictably produce this kind of result".
Others claim that "Clerical child sex abuse has nothing whatever to do with celibacy."
The truth, as is many cases, likely lies between these extremes, though it is cannot be neatly located on the scale from "causes the crisis" to "has nothing to do with it".
Leaving aside any empirical statistical evidence on the frequent of sexual abuse by celibate or non-celibate men, some aspects of celibacy would, taken on their own, suggest a connection between priestly celibacy and abuse, while others would suggest an inverse correlation (mandatory celibacy for priests countering the risk of someone abuser vulnerable persons).
Marriage as a remedy for concupiscence — suggestive of a connection between mandatory priestly celibacy and abuse
Marriage has long been described by Christian saints and writes as a remedy for concupiscence, by St. Augustine (see, for just one example, On Marriage and Concupiscence, Thomas Aquinas (see Summa theologiae, supplement, q. 42, article 3, Whether matrimony confers grace, and a multitude of others (see a selection of texts in the post Is marriage for the weak?). In this respect, it would not be surprising to find that those who are not in a position to legitimately satisfy sexual desire in marriage, are more likely to satisfy sexual desires in illegitimate ways, up to and including abusive ways. Celibacy does not make a man's sexual desires perverse or disordered; rather, his sexual desire is lacking order to begin with, being in the first place an instinctual drive, that must be governed by reason; the lack of the structured governance of that drive provided in marriage will, in the absence of contrary remedies, tend to lead to more disordered desires and acts.
Celibacy as freely chosen, involving abstinence even from legitimate sexual pleasure in marriage — suggestive of an inverse correlation between mandatory priestly celibacy and abuse
On the other hand, no one is forced to become a priest, and so, when we speak of priestly celibacy, we are not speaking of celibacy imposed randomly, independently of man's will, or even against man's will. Rather, it is a celibacy freely chosen (even if, in a particular instance, chosen principally as a condition or means to the desired end, the priesthood). If those who freely choose celibacy do so with adequate deliberation and a firm will to live it, if they belong to those "who can take it" (Matthew 19:12), we should, other things being equal, expect them to less frequently fall into sexual sin. For he is capable, or takes the means to render himself capable, of refraining from satisfying sexual desire in a legitimate manner in marriage, is much more capable of refraining from satisfying sexual desire in a sinful manner.
Celibacy as chosen by reason of being drawn to that way of life or not drawn to marriage — possibly suggestive of a connection between celibacy and abuse
No one is forced to become a priest. But also, in most cases, priests are, in the first instance, self-selected. Catholic communities and bishops could, in theory, come to men with the proposal, "we would like you to be a priest; are you willing to remain celibate for the rest of your life, study theology, to serve the Church in this diocese, etc.?" But, in many or most cases, the decisive initiative is taken by the men themselves who consider the priesthood. Given the association of the priesthood with celibacy, this has a unintended consequence: those who, for whatever reason, are not inclined to marriage — homosexuality, asexuality, sexual immaturity, sexual disorders — will be over-represented among applicants to the seminary. In the absence of an adequate mechanism to identify and exclude them, persons with certain sexual problems may also end up being over-represented in the presbyterate. And, very plausibly, some of those sexual problems will manifest themselves in distorted ways, including abusive ones.
Celibate priesthood as a special class — positive and negative aspects
A fourth point regarding celibacy is somewhat ambivalent: the discipline of celibacy tends to reinforce the image of the priesthood as a special class of Christians. This aspect of celibacy, might, in some times and places, contribute to a culture set firmly against all abuse, inasmuch as other priests who get wind of possible abuse are keen to uphold the reality of their class as a holy state, called in a special way to Christian virtue and holiness, and for whom, therefore, such sins are still more intolerable than they are in the case of lay persons. On the other hand, that the celibate priesthood makes up a special class may also have the opposite effect, lead to a culture permissive of abuse, because (1) one stands up for one's own, defends one's brother priests, assuming their innocence or downplaying their faults, because (2) one desires to uphold the image of the priestly state as a holy state, or because (3) the discrepancy in one's own life between the greater ideal of holiness to which one is called and one's actual life, causes one to misjudge the gravity of other sins; in the theological tradition, and expressly in the 1917 code of canon law, canon 132, clerics in major orders are so obliged to chastity that to sin against it is to be guilty of sacrilege (the notion behind this is that the priest's whole self, including his body, is dedicated to the Lord as something holy, so to sin against it is to violate what is holy); a priest guilty of habitual impurity, whether by fornication, adultery, masturbation, pornography, or impure thoughts, could possibly become thereby less inhibited from a crime such as abusing minors than a lay person guilty of the same habitual impurity would; similarly, a priest guilty of such impurity, whether occasional or habitual, may view such a crime by another priest less seriously than a lay person would.
Various problematic issues arising in connection with the priesthood as a special case are often treated under the notion of clericalism, by pope Francis (Letter of His Holiness Pope Francis to the People of God), and others (e.g., Sexual abuse and the culture of clericalism).
In view of these considerations, some of which, taken on their own, would suggest a link between celibacy and abuse, while others would suggest that celibate priests might be less likely to be sexually abusive, it is not too surprising, that, on some accounting, sexual abuse of minors (or at least behavior evoking a serious accusation of such abuse) is as common by married Anglican clergy as by celibate roman catholic clergy. (See, e.g. Does Celibacy Contribute to Clerical Sex Abuse? by Richard Cross, and the therein reference studies.)
At any rate, the issue is much more complex than "celibacy is unrelated to the issue of sexual abuse" or "celibacy is a principal cause of sexual abuse".