Up until recently, homosexuality was considered a disease as well.
And gay men were also considered predators.
And there's statistically a lot of examples of gay men and women who were also sexually abused as children. It's not to say that anyone who's abused will be gay, or a pedophile, or whatever, but that the same correlation is also there, so I don't think that's a reasonable or relevant distinction. I was abused when I was younger and not only do I not find children attractive but I can't even stand their presences.
As for the predatory aspect, you have a minority group who are taught that their urges are abhorrent from every angle, are treated worse than murderers if caught and convicted and generally have to suppress or hide this aspect of their desires. Psychologically it's terrible and ends up creating a fracturing level of mental stress. Coupled with the fact that their targets are vulnerable and incapable of consenting to what's being done with them and you have someone who, when they do act out their fantasies, generally does so violently and destructively because socially they know that everyone else considers them evil.
Then there is even degrees socially. Up until recently child brides were commonplace. The age of consent being 18 was only recent, and even that varies across state lines. Some countries today still have limits that I personally think are ridiculously young. What is considered too young in the US is normal in other countries and other cultures.
I'm loathe to have any of this be misconstrued or have anyone think I'm excusing pedophilia. The real issue is that of consent, and I won't disagree with anyone that children lack the experience or mental acuity to understand what they're doing. That is the issue for me, but I do believe that the same factors that made me gay are similar to the process that makes you straight or makes someone attracted to having sex with a horse. And when people talk about curing pedophilia it makes me uncomfortable because I think it's really a short step to trying to cure gay people.
Now as for solutions instead... I don't really have one. I don't know what it must be like to live that way, and I'm happy I don't have to.