Then what IS it about? I don't understand why it makes any difference if someone calls a child molester a pedophile.
I have a problem with it because it can perpetuate the idea of a "boogeyman." It actually places more emphasis on motive, in my opinion, because it puts the attention on the idea that "sickos" are the ones who target children.
In reality, sometimes young people are targeted by abusers who don't fit the diagnostic criteria for pedophilia. And some abuse isn't pedophilia by definition (if the victim isn't prepubescent). A lot of children are abused by people who appear to be perfectly capable of experiencing attraction to adults, and who live "normal" lives. There's not one type of child molester any more than there's one type of domestic abuser.
I'm also 100% against sex offender registries. They're useless at best and actively harmful at worst. People have been put on them, or threatened with being put in them, for everything from peeing in public to sharing nude photos of themselves as a teen to inappropriate childhood sexual behavior that doesn't usually lead to lifelong offending. The idea behind registries is that sex offenders are a lifelong danger, which is a direct consequence of treating sex crimes and paraphilias as synonymous. Pedophiles have a condition that's very difficult to overcome, but not all sex offenders (even ones guilty of crimes that are actually serious, like rape) are habitual, compulsive predators. You might as well have a registry of drug dealers or robbers.