The term commonly used to describe someone who doesn't care about or show empathy towards others' feelings is "lack of empathy" or "empathy deficit." Empathy is the ability to understand and share the feelings and emotions of others, and individuals who lack this ability may be seen as unsympathetic or indifferent to the emotions of those around them.
In some cases, people with a lack of empathy may exhibit traits associated with certain personality disorders, such as narcissistic personality disorder or antisocial personality disorder. However, it's essential to remember that making a diagnosis requires a thorough evaluation by a qualified mental health professional.
It's important to differentiate between someone who genuinely lacks empathy and individuals who might struggle with expressing their emotions or have difficulty connecting emotionally due to their own past experiences or personal challenges. Empathy can be a complex trait influenced by various factors, including upbringing, socialization, and individual differences.