Empathy is like a belly button because there is an outside in and inside out quality to it.
The practice of nonviolent communication would say that empathy is inside out. Empathy comes from self-empathy and putting yourself in the other’s position. NVC training emphasizes that you are NOT showing empathy when you tell someone of a similar experience that happened to you.
I believe this is true but empathy also has an outside in quality. I/we develop empathy by our own direct experience. The trick is to use that experience without ego.