Samuraisan - "I just cannot understand how anyone can be a paedophile . I just can't . I think it's the most deplorable crime, the absolute worst. What on earth makes them like this ?"
Although the effect is far more horrible and damaging than comparable character traits, the roots of the impulses are the same as any other human impulse.
You can line up the impulse under the same list as - what makes some people like Marmite, or trainspotting, or opera, or eating offal ... the list goes on.
It is impossible to realistically put yourself in the mind set of someone who thinks differently about any of the above list - and paedophilia - because you would need to be that person, with their impulses and experiences, and of course, you are not.
So there is no simple answer to your question.
Because of the devastating damage that this predilection causes to its victims, and the innocence of those victims, it is very easy to slip into thought processes that involve labelling such individuals as 'monsters', and 'demons', and dreaming all sorts of elaborate an painful revenges.
Before anyone starts foaming at the mouth, I neither defend or excuse such behaviour, I merely seek to answer the point made by Samuraisan - there is no reasonable explanation, because it is not the behaviour of a rational mind, and trying to rationalise it will go nowhere, except to hurt your head.