The desires of paedophilia are an illness.
Acting on those desires is a crime.
I remember having a similar argument with a professor in a college psychology class. He stated that pedophilia (like most sexual urges) is irresistible. I argued that it was resistible and that psychologists and psychiatrists suffered from a bias because of the (rightful) disgust pedophilia is seen, that very few pedophiles go for treatment because of resisted urges. Instead only those who have been criminally caught are medically treated. Thus since psychologists only see those who did not resist they assume that no one can resist. Neither one of us convinced the other, but hopefully some of my classmates reconsidered their blindly nodding approval of the professor.