It's hard to pull apart empathy from compassion. What is really clear is that we innately care for other people at least to some extent.
By “empathy,” some people mean everything that is good - compassion, kindness, warmth, love, being a mensch, changing the world - and I'm for all of those things. I'm not a monster.
People differ in where they direct their empathy and their compassion. Many people are intensely concerned about the suffering of non-human animals, and some do not care at all. There are cultural differences.
I think we should really discourage this sort of empathic engagement when it comes to making moral decisions. I think we should focus on something like compassion, on getting people to care more for others without putting ourselves in their shoes.
Some people think that without that spark of empathy we would do nothing, but that's just flat-out wrong. You could feel compassion for somebody without the spark of empathy.