An unwillingness to empathize is different than being unable to do so.
We generally assume that narcissistic people lack empathy, as though they are missing a certain brain function. Granted, such thinking can make us feel better when a relationship dissolves. However, in some circumstances, an individual with a narcissistic personality disorder may display empathy, which can be confusing.
Consider the possibility that narcissists are consciously and unconsciously unwilling to empathize, rather than lacking the capacity to do so. The notion that a person can have a capacity for empathy, yet not be empathically responsive, may be useful for understanding the personality characteristics of people we label as narcissistic.
Empathy is the capacity to think and feel oneself into the inner life of another person.  Some regard empathy as a vicarious affective response based on the awareness of another person’s emotional state.  Many definitions of empathy include the concept of perspective-taking—emotionally or cognitively seeing things from the other person’s position.  Thus, empathy can involve both a cognitive process (the ability to understand another person’s view in terms of what the other is thinking or feeling) and an experiential process (resonating with another person’s emotional response).
A lack of empathy is often considered to be one of the distinctive features of narcissism. However, this is not entirely the case. The criteria for the formal psychiatric diagnosis of narcissistic personality disorder in the Diagnostic and Statistical Manual of Mental Disorders of the American Psychiatric Association includes “lacks empathy,” but this designation has a critical qualifier: namely, “is unwilling to recognize or identify with the feelings and needs of others.”  An unwillingness to empathize with another person is not the same as being unable to empathize with another person.
Some researchers have found that the cognitive functioning necessary for empathy, such as the ability to role-play or take another person’s perspective, occurs in a different location of the brain than the emotional aspects of empathy, such as sensitivity to what another person is feeling or experiencing.  Whether one is narcissistic or not, our brains simulate the feelings of those around us. This ability to mimic another’s feelings enables us to reconstruct within us what other people may be experiencing. 
Given the many and complicated interactions we have with others throughout our lives, the ability to automatically understand what is going on with someone else is a crucial skill for successful social functioning. Some studies have shown a relationship between narcissism and deficient emotional empathy, but that narcissists, nevertheless, can recognize and react to the suffering of others, even if they are motivated to disregard such distress in other people. 
The capacity to empathize does not preclude its use for bad behavior. Descriptions of empathy have included the notion that empathy can be used for destructive purposes.   Thus, people who have a narcissistic personality may consciously or unconsciously be motivated to withhold an empathic response to control a partner or to justify their behavior. They may exploit their understanding of another’s emotional state to manipulate that person. Using their empathy manipulatively, people with narcissistic pathology know how to evoke insecurity in their partners and provoke attachment anxiety. 
The concept that a person can have the capacity for empathy, yet not be empathic in his or her response, is also important for understanding how people with a narcissistic personality disorder may protect themselves. Consider for a moment that these people do not really lack empathy, but instead, their vulnerability limits their freedom to express it. Thus, they have an unwillingness to empathize rather than a lack of empathy.
Many people who seem to lack empathy for the other humans in their lives can express enormous sympathy and compassion for their pets, and they may overtly express empathy regarding an ill or injured animal. In such situations, someone with a narcissistic personality may feel emotionally safe and capable of vulnerability. The subjective experience of trust can be a powerful tool for narcissists that reduces perceived threats and allows them to attend to the needs and feelings of others. 
There is evidence indicating that narcissistic individuals are hyper-sensitive to information that could cause them psychological distress, but at the same time, they may be oblivious to such information at the level of conscious awareness.  Interpersonally, where someone with narcissistic traits experiences helplessness or vulnerability, they are likely to withhold an empathic response automatically, appearing cold-hearted or as refusing to take responsibility for hurtful behavior. How do we understand why someone would appear to lack empathy or have an unwillingness to empathize? The answer involves a personality organization that over a lifetime has been scripted to avoid shame.
When emotions occur in persistent or repeated forms, we consider them as dispositional characteristics of the individual or personality traits—situations that typically activate a coherent pattern of interacting emotions or scripted behaviors. Unfortunately, the language of personality traits overshadows the emotional states that motivate the behavior.  For example, we generally consider narcissism as having to do with behaviors or traits, such as grandiosity, entitlement, and a lack of empathy, but this obscures how these behaviors and traits are patterned responses to specific emotional experiences. Shame is the central emotional experience of narcissism, and narcissistic disorders reflect behaviors that serve to disavow and regulate shame.  
Since an empathic response often involves an unconscious assessment of one’s vulnerability to experiencing shame, the narcissist’s inhibition of an empathic response (“unwillingness”) may simply be self-protective. This also points to the affective limitations that accompany narcissistic personality disorder. Narcissists do not consciously feel a lack of empathy or an unwillingness to empathize. Instead, in many situations where one might expect them to empathize, their limitations activate a sense of helplessness (imagined vulnerability) followed by scripted responses to shame, such as shame-fear (fear of loss of face) or shame-rage (protection from some imagined trauma from the past). 
Thus, if you are involved with someone who is motivated by shame to be consciously or unconsciously unwilling to empathize with what you feel, your task is to protect yourself. Blaming heartache on a former partner’s “lack of empathy,” for example, is a mistake. You may be responding to your own shame by attacking someone who could not provide what you needed in the first place, due to their restricted emotional freedom. Instead, by accepting your disappointment and looking inside yourself, you can learn.
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