Weirdly the book "How To Talk So Kids Will Listen..." can help. I don't think that to be empathetic you definitely have to understand/know/be able to imagine exactly how somebody is feeling, it's just that you accept they may have different feelings to you. ie just because you wouldn't be upset by a particular comment, situation, doesn't mean that they are being silly to be upset by it. Putting yourself in someone else's shoes is part of it but it's not the whole picture.
The stuff about validating feelings and empathetic listening in chapter 1 of How To Talk works for talking to anybody of any age, not just children. It's about not saying things like "You're worrying over nothing, I'm sure it'll be fine!" instead you can reflect back by saying "You sound really worried about that." or "Oh that sounds really tough".
I think the automatic knowing/understanding how someone feels is just a character trait and can't be learned or taught, but being sensitive and aware and accepting of other people's feelings is definitely possible to learn, not that hard either.
I think that's what your therapist might have meant? That you don't have natural empathy (which is fine, I think most people don't know automatically what another is feeling), but also that you've never learnt the other part, about acknowledging, accepting, thinking about. For example a truly unempathetic person might do something that annoys or upsets a friend, thinking "Well I wouldn't mind if she did it to me, so it's okay!" - using empathy, you'd be able to think "Actually, this friend might find that thing hurtful." The "natural" kind of empathy isn't much use here - the "natural" empath who isn't doing the "thinking" empathy might not realise until the friend is hurt, at which point they'd feel terrible, whereas a totally non empathetic person might not realise at all.
Hope that makes sense and isn't more confusing
