Pædophilia is classically viewed as a disease that can be treated, albeit with significant difficulty and with varying results. Sometimes treatment can help, sometimes it doesn't, but that's a whole doctorate piece right there.
However.
The natural rate of pædophilic tendencies (people who react to pædophilic stimuli) is higher than you might think - it's 20 to 25%. Let me repeat that:
The natural rate of pædophilic tendencies is 20 to 25%.
Clearly it is illogical to label a quarter of all known humanity as mentally ill! (This may be an understatement - the classical rate is 27.7% and some studies quote a figure as high as 32.5%, implicating some two billion people!) This is the argument used to counter the notion that pædophilia is a psychiatric condition.
Nowadays the condition is viewed as a "distortion", closely bound to aspects of self-control. The vast majority of those who exhibit "strong" tendencies towards pædophilia do NOT offend, ever. I'll repeat that too:
The vast majority of pædophiles do NOT offend, ever.
Of course, the definition of pædophilia is part of the problem. The figures quoted above apply to people who exhibit sexual arousal to pædophilic stimuli that equals or exceeds their arousal to adult stimuli. However, to be classified clinically as a pædophile, one must exhibit, over a period of at least 6 months, recurrent, intense sexually arousing fantasies, sexual urges, or behaviors involving sexual activity with a prepubescent child or children (generally age 13 years or younger). In addition, one must be at least 16 years old and must exhibit said tendencies towards a person 5 years or greater their difference.
Since it is apparent that pædophilia is a condition as opposed to an illness, one should therefore view those with the condition with a strong sense of pity - they never chose to have the condition and must bury it and stamp upon it utterly every day of their long lives.
Not that I argue for pity in place of punishment for those who do offend. It is not believed that it is possible to harbour such an inclination so strong as to be undeniable. In other words, offenders have the capacity to deny their base desires and do not do so.
Those with such a strong inclination towards pædophilia that they end up offending should therefore be segregated from society for reasons of safety. At this time treatment is, as stated above, difficult and varying in effectiveness, so until we can improve this incarceration would have to be for life.
Half the problem is the stigma. If people knew that the vast majority of pædophiles were afflicted against their own choice and had to suffer with it day and and day out and did not offend, our problems would be half solved! Those with the condition would, if not for the stigma, submit themselves for treatment, that which we know and possibly benefit. Those who did not respond could be isolated on friendly terms - offences would be heavily reduced, but for that stigma.
Mass culls are not the answer in a civilised world to a problem so little understood or even realised.