In general, empathy can be either an evolved behaviour, a learned behaviour, or both.

In humans this is largely-but-probably-not-exclusively socialized behaviour. Most cases of (human and non-abused) feral children exhibit behaviour that is not particularly compatible with empathy.

I shared my rationale for why we "haven't always had this capacity" a few comments up this thread, and you seemed to agree with it before immediately making the contradicting statement.

It was very recently evolution wise that humans started to keep animals as pets, before then we just hunted and ate animals. We would empathize as much with those animals as cats did with mice.