Because there are different brain regions for cognitive (taking another point of view) and emotional (feeling with another person) empathy, injuries can result in impairments in one and not the other.
If emotional empathy pathways are impaired, impose a highly structured cognitive empathy program beginning at a young age -for home and for school. Remember the saying in Lawrence of Arabia: "With Major Lawrence, mercy is a passion. With me, it is merely good manners. You may judge which motive is the most reliable." Some parents may exhaust themselves in battles with their children, trying to appeal to the emotional side of a child's empathy, but some children may really have broken pathways. Cognitive empathy can make up for a lot, as long as it is backed up by constant practice so that it becomes a part of a child's character.
Adolescence: The teaching of empathy for high school and college students: testing Rogerian methods with the interpersonal reactivity index
APA Public Communications: What Makes Kids Care?
The caring child: How to teach empathy