Do people feel impotent when arguing with someone able to do Emotional detachment? Some people who experienced negative emotions after being forced in their childhood often develop a passive-aggressive behaviour as a form of self defence against whoever is trying to manipulate / force them.

Instead of a simple assertive "no" in a dispute they tend to overreact sometimes in a passive-aggressive way, i.e. through emotional detachment. 

They are usually aware this can hurt the person who is angry with them but use Techniques of neutralization to feel "OK".

But why do people tend to be hurt by this kind of passive aggressive behavior? Does this happen only to people with obsessive / narcissistic personality trait?
The answer to this question is in the link to passive-aggressive behaviour I provided in your question.


  In conflict theory, passive-aggressive behavior can resemble a behaviour better described as catty, as it consists of deliberate, active, but carefully veiled hostile acts which are distinctively different in character from the non-assertive style of passive resistance.


When faced with any hostility, most people would feel hurt

Examples given in the link to passive-aggressiveness in the workplace including


  [deliberately] 'forgetting' to do something, chronic lateness, and intentional inefficiency.


leads to others having to pick up the slack.  This not only hurts people - knowing that the passive-aggressor could have done it but didn't - but it also leads to resentment by those picking up the slack and can lead to low morale leading to more problems in the workplace.  And it can hurt anyone, not just those with obsessive/narcissistic traits.