Mark Vernon delineates some:
Empathy too is often taken to be an unalloyed good thing. And yet, as Colin Frith, emeritus professor at UCL, recently told me, an empathic feeling might as easily lead to an unkind response of fight or flight as a good response of compassion. Feeling viscerally upset by someone else's pain might make you turn your back. Alternatively, collective empathy with my in-group can lead to collective animosity towards those perceived as others. Such empathy powers war. The risk is that my compassion for some leads to self-righteous anger at others.
The Dish 