It doesn't help that there are a good number of cases of horrible child abuse (some of which are commited by pedophiles).
The "some" should be pointed out to be possibly no more than 20%. Most cases of actual child abuse occur in the home of the insular nuclear family unit by teleiophiles on power-trips, not by the pedophile living down the street. The former are opportunistic abusers.
In regards to truly horrific cases of child kidnappings by strangers, these are psychotic individuals who are anything but typical MAPs (if any of them are actually MAPs as we understand it at all), and as terribly tragic as each incident is, it has always been a very rare type of crime.