I was listening to someone talk about how they respond 'sympathetically" to customers and as I listened to her describing being sympathetic, I realized that she was not listening to the other person but reacting to what she was hearing. I believe that being sympathetic means that we respond personally based on our own reaction to what's been said. This seems to make sympathy more about our reaction to others and not about what other people are experiencing. So, sympathy is not really about listening to others even though having someone listening to them is what seems helpful for people who are struggling with emotional pain.
However, many of my patients have expressed feeling like they were "not helping at all" when they "only" were able to listen when they were with friends or family who were grieving a loss. Often we feel that we are not being helpful if all we are doing is listening. However, it can feel stressful to listen to someone who is experiencing emotional pain. Maybe it is this stress that we feel listening to others who are experiencing emotional pain that leads us to offer sympathy. So we don't have to listen any more in order to relieve our own feelings of stress.