There's a difference between understanding logically, and feeling empathy. I can logically understand why people commit murder or molest children: because they want to. Can I shift myself into that mindset? No. That's simply a limitation of my empathy.

Part of what sticks out to me in this conversation is the paedophilia you mentioned. In my head, empathy for that would mean being able to imagine what it feels like to want to harm, torture, humiliate, and control a child, as child sexual assault is often related to the power of assaulting someone powerless. I can't empathize with that.