I've also heard theories that our empathy is actually a hunting tool. If we were to lose our prey, say in the brush around a water source, we could put ourselves in its mind. From there, we could empathize and predict their actions, and so follow them, even without tracks. From the prey's perspective, they finally lost us and escaped, they are exhausted and overheating, but alive. Suddenly the predictor re-emerges, and the chase is back on.

Vegetarianism being a fairly unique human trait suddenly makes sense, from this perspective. A lion doesn't really need to get into the mind of their prey, and so empathising with them is actually a negative. For humans it was a critical tool. It's only secondary that we turned it on each other, allowing for super-tribes to function.