There is a big difference between a broken will and a deviant will. This came up recently in a discussion with someone over the arrest of a pedophile. The person with whom I was speaking with called pedophilia an 'addiction.' I said it was not, and here's why.
A pedophile is someone who's will is guided by a desire to abuse children, yet he does not see his actions as harmful or regrettable. If you have ever met a pedophile, they are genuinely unrepentant even after a great deal of treatment because overcoming an 'unnatural attraction' is extremely difficult.
Our deepest desires are entangled in levels of our being that the logical mind cannot easily reach. Usually, we end up trying to 'repress' these areas, which is about all you can do. This is why few people can be successfully 'treated' for pedophilia. Of course, there are different reasons for pedophilia arising in a person, and there will always be those exceptions to the rule that are able to break free, but they are rare.
The same is true about other attractions, such as homosexuality. I don't think there is a one-size-fits-all explanation as to why 3-5% of us have this desire, but then again sexual attraction is hard enough to understand on its own because it also occurs so deep within us. As modern people dominated by logical thinking, it is virtually inaccessible. Yes, there are some that can come out of this type of attraction, but I think it is foolish to assume that every homosexual is 'curable,' especially if they don't want to be cured.
The attraction to addiction is more complex: yes, there must be an 'attractive' aspect to the addiction. The Big Book of AA first used the concept of 'allergy' to describe this experience. By allergy, they mean that alcohol releases a certain series of chemicals within the brain of the alcoholic that normal people do not get or experience the same way. The effect of alcohol induces more pleasure in the alcoholic than in other people, and this unusual effect is summarized as an 'allergy.'
This allergy alone, however, is not enough. That's where the comparison ends with deviance. You see, just because you have an allergic reaction to something does not mean that you are attracted to it. You can be attracted to the effect, but not the substance itself. This is why alcoholics will go from being very choosy about their drink of choice to eventually drinking anything they can get their hands on.
This ability to separate substance from effect is very important in recovery, when the second aspect of addiction comes to light: the mental vulnerability caused by pre-existing suffering. Addiction arises when the pre-addict combines his suffering with the allergic reaction which wipes out the suffering. Now, you have an explosive combination.
The loss of will in the addict comes with the escalation of suffering which is only masked by the allergic reaction. In essence, in order to not experience the overwhelming suffering, the addict is obliged to have repeated allergic reactions. More pain, more reactions. This escalation is behind addiction.
Now, recovery means several things. First is the curing of the suffering, but the second is almost co-occurring: the realization that the object of desire is in fact not the problem, but the effect is. The alcoholic must realize his escapism in the bottle before he can truly recover. Once this is realized, the obsession to drink ends as he emerges from his pain using the 12 Steps.
Notice that the 12 Steps do not command the alcoholic to stop drinking. The will goes back to its natural state once the pain is alleviated and the attraction to the effect is realized.
In the case of a pedophile, the natural state of the will inclines towards pedophilia (unless we are talking about one of those rare exceptions). A deviant will is broken from the beginning in a way an addict's will is not, which is why the Steps talk about being 'restored to sanity.' A deviant will cannot be restored to anything but deviance.
An addict is not a deviant with a deviant will, but a broken person with a broken will.
Of course, we hope that pedophiles and other deviants can learn to manage their broken wills with God's help and their inner goodness with which all mankind is created. But, it is indeed a much harder road.