"Emotional sensitivity" refers to the ability to be aware of and understand one's own emotions and the emotions of others. It means being perceptive and responsive to emotional cues in oneself and in those around you. Full definition
Children's levels of emotional sensitivity vary, and when some children are separated from positive people in their lives they can feel distressed. (kidsmatter.edu.au)
The factors included academic challenges, suggesting a learning disability; behavioral challenges, suggesting an emotional disorder; or academic strengths with emotional sensitivity, suggesting that he is gifted and talented. (sciencedaily.com)
His sharp, emotional sensitivity makes him an ideal therapy dog. (platpets.com)