As a pedophile myself, I can confirm that yes, we're born with the attraction same as anybody else. Unfortunately, our history is a bit more tarnished compared to gay rights in general. See, in the old days, two gay men just found each other and broke the rules, simple enough. End of story.
But for pedophiles, it's not that simple. For one thing, it's rare that some willing youth just randomly finds us and a relationship is allowed to develop naturally. For another, society instills (or used to, not so much these days but still) the idea that all children should obey all adults at all times, creating a power imbalance that's very unhealthy for a romantic relationship. A pedophile who really buys into that idea can be dangerous, because they see a child as subservient and therefore someone who should just indulge their sexual desires "because they say so". (Obviously, I'm not a supporter of that idea.)
A sexual drive is like a craving for food - the longer you go without eating, the hungrier you get. So with no outlet and a dominant mindset, a pedophile can literally become the equivalent of a guy trapped on a desert island for two weeks with no food and water. Teleport that guy into the center of a mall food court and he's going to grab the nearest hamburger, regardless of whether it belongs to someone else or if it's right to do so. By the same token, some pedophiles "snap" when a circumstance comes along that gives them access to a child, and the result is disastrous.
Good therapy is all about preventing those snaps, making sure the pedophile finds a healthy (and legal) outlet for his or her sexuality. They don't try to "cure" it - they know just as well as anyone that it can't be "cured", only suppressed.
So, y'know, with all the people who've been scarred and damaged over the years by pedophiles who either snapped or felt entitled, it's not a surprise that no one's leaping to legalize it. It also doesn't help that those who had positive sexual experiences with adults when they were children can never legally talk about it, because even 20 or 30 years later, their adult lover can be prosecuted for that relationship even over the objections of the child (or former child). That's the best first step, IMHO - change the law so that only the children themselves can press charges. You'd have a few children being unduly persuaded the "wrong" way out of fear on both sides (kids who don't press charges because of fear of the adult sleeping with them, and kids who do press charges because of fear of their parents or cops), but we'd start to hear the positive stories come out and I bet there are a TON of them. We'd also be able to have a much more open dialogue on the subject in general.