@CosmicTrigger I think I would change that a little and say that what we call evil is most typically the absence of *compassion*, not empathy.
Empathy asks the question "how would I feel in that situation?" Empathy is the underlying logic of the Golden Rule, to treat others how YOU would want to be treated. And that's all well and good but that means the empathy is ultimately still self-centered and a bit solipsistic: it leaves no room for people whose desires and values and even modes of cognition are completely and utterly different from you, who truly want different things than you want, and truly feel different in some situation then you would feel. I think overactive and controlling empathy is actually what produces a lot of the "we have to stop the trans from mutilating their bodies" stuff, for instance: the average man can't imagine wanting to get vaginoplasty (nor the average woman mastectomy) and so when they try to have empathy for a trans woman (or man) it doesn't work.
Moreover, empathy leads to pity and pity leads to hierarchies of domination through charity and infantilization.
Furthermore, empathy is a fickle emotion, and I don't think conceptualizing morality in terms of feeling the right emotions instead of actions and habits and ways of thinking is a good idea. After all, empathy is an emotion that not all people are capable of. And I think it is incredibly ableist and pathologizing to insist that all sociopaths must inherently be evil since they can't experience empathy. That's simply not true in my experience.
Meanwhile compassion is the act of *choosing* to care about someone else's *actual* emotions. It is less an emotion than a character trait and habit that can be built up through practice and genuine desire to be better, and it does not suffer from the failure modes of empathy.