An incredibly late reply, but I might as well post it:
Empathy for pedophiles (that have not acted out on their desires) stems from the now increasingly accepted position that they have no control over their sexual desire. They have to live with something they know is wrong, can never enjoy a healthy, consensual sexual relationship like the majority of us, and risk losing their job, friends, and family if their secret is found out. This must be a living hell for those who want to be a part of society, yet know they can never change their sexual orientation-even if they wanted to- and therefore, cannot ever truly belong. They see the hate that society gives them, and many hate themselves, as a result.
At the same time, most realize that demonizing pedophiles has a net negative effect on the prevention of child sexual abuse. Of course, those who can't control themselves will still be offenders, but those who are struggling have less incentive to not hold back when they see an aggressive environment that despises them. Eventually, they may develop an attitude where they just don't care about the moral ramifications because they are not imparted by the public any sense of humanity, and thus, feel like they are not bound by it. Offering them therapy, while pursuing research into the subject to possibly fix the cause neurologically will hopefully result in a decrease of offenses, and will also give them more fulfilling lives (although, I know most people don't care about that).
Here's some research that points to a biological origin of pedophilia (link directs to U of Toronto's James Cantor PhD's blog and findings):
http://individual.utoronto.ca/james_cantor/blog2.html
I hope this didn't come off as standoffish.