We're carrying on a conversation from the past few days, feel free to get caught up before reading this one.
Empathy for offenders (when and where it's possible) begins with seeing ourselves as we truly are: people who are just as capable of creating offense as receiving it. Unfortunately, this is not something that can be taught and learned, it can only be discovered. Sadly, we tend to discover this truth only when we find ourselves on the outside of a group, banished, with no false group identity to protect us from seeing ourselves as we really are (this is, again, Girard's thought).
When we recognize the truth about ourselves, then we recognize that there is no great divide between ourselves and other people who cause harm (even, perhaps, our offenders). Now, again, I'm not suggesting there is no moral distinction between a victim of rape and a rapist but, I am suggesting that, over the course of a lifetime, all of us cause harm and are capable of much more. If we discover this about ourselves, then we don't see ourselves as people above wrongdoing.
The goal in viewing ourselves as wrongdoers is not to shame ourselves for being wrongdoers but to simply see ourselves accurately and to discover exactly how much grace and love we receive from God (and, hopefully, community). We do not need to see ourselves only as wrongdoers but as people who miss the mark, people who struggle to live out our certain way of seeing. This is what allows us to empathize with others. We recognize our struggle, and that means we can recognize that others struggle as well. Most people do not get up in the morning with the intention of ruining people's lives. There are, of course, exceptions, but most people cause harm because they are struggling. This means they are not so different from ourselves.
Side note: Of course we’re not going to empathize with every offender and we do not need to empathize with every offender. However, it never hurts to learn to view ourselves accurately and to find a more nuanced perspective on the world in the process. In this case, we discover that we are not only victims of our offenders. Our identity can be much larger, if we can see ourselves accurately. Learning to see that offenders have an identity beyond their offenses is a tangential benefit.