Personally, I think that if you star "teaching" empathy at a young age, then yes it can be taught. The article "Can You Teach People to Have Empathy" tells how "listening out for people's feeling and needs... gives them a sense of being understood"(Radical Listening, 3). I expect this to be true. When I am venting to someone; whether it be my friends or family, and I know they are listening, I have a sense of being acknowledged. "According to the latest neuroscience research, 98% of people have the ability to empathize wired into their brains- an in-built capacity for stepping into the shoes of others and understanding their feelings and perspectives"( page 1). This clearly states that when you are born you can already process empathy and peoples emotions. Therefor, it only takes a little bit of teaching for you to access that part of your brain.
"We learn empathy through stories and people coming into our lives and saying stop for a second and think about what it is like to be someone else in this situation; stop and try to imagine that person's life for a moment"(Bystander Revolution: John Green). A lot of kids learn empathy through child book situations and take that to apply it to their own life. Children learn best with examples and what best way to teach a child about empathy through a story that will stay with them.