It's easy to extrapolate people's motivations and beliefs, aka jump to conclusions, because you think you understand what you're hearing. Instead, take in and verify what they're saying without agreeing or disagreeing. When you say non-judgmentally "I'm hearing that you think/feel/experienced ...", you'll be amazed how often they tell you that you misunderstood. That's totally fine, because they'll correct you, and after a few rounds of that you'll really get where they're coming from and they'll know it, which is what empathy's all about. You don't need or want to take on their feelings and beliefs though, because integrity is an important part of empathy. So a respectful "that's really important to you"-like comment again makes them feel understood without in the least compromising your own principles. Once you and they both are certain you get where they're coming form, then the conversation can move on from there as appropriate.