I believe you are born with empathy.

I raised three children.

Two seemed naturally inclined to empathy and I really don't think I did more than cultivate what was already there. A lead by example sort of thing. I certainly expected a reasonably minimum high standard of empathy, feelings, and taking others into account.

Unfortunately it wasn't so with the third. My step son has not an ounce of empathy within him - and he couldn't be taught it either. When he stole for example or committed acts of violence he had no thought for his victims. He did things like steal because he felt he deserved the money or object. It failed to occur to him what this was doing to those he stole from or hurt. No matter how much I tried to show him the impact of his actions on others the more he stared blankly in utter confusion by what I was saying. Suggesting he lace himself in the other's shoes he couldn't fathom what the point of that was. He simply deserved the object of his desire, felt wronged that he was denied it, and that he was justified in obtaining it.

I raised all three with the same nurturing, support and expectations, yet I got completely different results. So yes, I believe empathy is something innately within us.