Oh, wouldn't it be nice if all those loving parents just put the smack down on their obviously under-disciplined children? You haven't parented children. Come back with an informed opinion when you have.
Now speaking to the problems...
1) The term "pedophile" in a medical sense actually refers to people who are attracted to pre-pubescent children . Clearly this is a problem since 9 year olds can't reproduce.
2) The term "pedophile" in a more of a legal sense refers to people attracted to people under a certain age.(18 being common, but actually ranges to anywhere from 12 to 20).
Think about this for a moment: a range that differs by some 80% of its base value, as the basis of whether or not we should ruin somebody's life. 12 is legal in some places, in others you have to be almost 2x as old to afford the same legal protections! Clearly, the age of "adult" is an imprecise measurement, at the very least.
Biologically speaking, it's appropriate for men to be attracted to young females. They are healthy, don't already have children, and are likely to be available for bearing children. If you are a guy and you want to generate posterity, paying particular attention to newly minted young women is a particularly successful strategy. 200 years ago, it was pretty common for a young woman to be wed at 14, and an 18 year old unwed woman was regarded to be almost a spinster. Life was simple, life expectancies short, rules weren't so arbitrary.
Enter civilization, which lengthens lifespans but doesn't lengthen puberty. Abstract ideas create complex hard rules somewhat divorced from individual situations. Life is more complex, and the ramifications of a bad decision can be much worse, and it takes much longer for people to be truly cognizant of the effects of their actions.
But millions of years of evolution (or a moody, jealous god, your choice) have created a life form that is hard-wired to reproduce at about age 15 to 16, while the circumstances of that life form in its present circumstance has the real, ideal age of reproduction some 10 years later. Young people are impressionable and easily manipulated, and society seeks to defend their decisions by letting them incubate longer before making major decisions.
Folks, this situation just isn't going to end well for everyone.
While we should definitely work to defend young, newly sexually active people from the manipulations of far more experienced adults, we shouldn't ruin the lives of people who otherwise do what they are hard wired to do. And we certainly shouldn't group them with people who have an actual, diagnosed mental disorder.
I'm a father of adult children. One of my sons had a healthy, sexual relationship with a young lady 4 years, 3 months his junior. It was a courteous, long-term relationship, and he was civil and polite the entire time. It was terrifying to me, and there was precious little I could do about it. He was legally an adult, but had any authorities found out about it, could have face serious legal consequences, including being branded a "sexual offender" for life, treated as a diseased sexual deviant that he is not.
Try telling my kid no? Puleeeeaaaase.... your ignorance is part of the problem.