Very often, empathy seems to be characterized as part of the arsenal of peace and love. Yet, as I have written here before, empathy is neutral and can be used for good or bad. The peace it furthers may be embodied in understanding, forgiveness, and conciliation; or the kind promoted by a Colt Peacemaker®. And all shades in between.
A post in Big Think gives us a very handy way to distinguish between two kinds of empathy: Call them "hot and cold empathy." One is an "abstract, nerveless ... cognitive skill set," and the other is the "touchy-feely type." The former is part of the skill set of many, if not most, psychopaths.
So, if someone calls you empathetic or empathic, wouldn't you want to know if she means hot or cold? Maybe not.
Note: In this Big Think post, the neuroanatomy gets a bit confused, and lately this particular confusion seems to be rampant. The lizard brain is not the same as the amygdala; the amygdala is in the limbic system, not in the reptile or lizard brain.