Nate Miller yes I believe that empathy can be taught. Did you watch the short video?
First, one has to be in the right mindset, i.e. calm, relaxed, and unthreatened. In the case of your interaction on Facebook, sounds like the other person or both of you were on the defensive. In that moment the logical brain (pre-frontal cortex) is being taken over by the ancient brains (comfort and safety).
It’s only from a place of calm that you can practice empathy, and a good practice is to pretend. Imagine someone else’s suffering. How do you think they feel? How would that feel if it were happening to you? How would you simply be there, without judgement, without offering a fix, to allow them to express to you how they are feeling?
It’s not always easy! We are trained to fix, to offer a solution. But the best solutions come from the individual (which is why I love coaching, since it helps the person being coached find their own answers), but in the case of trauma, this is not the time for a fix. It’s a time for compassion and empathy.