Carl Jung wrote that we all have a "shadow" within us. That is, we have a negative side to our character that we seek to hide and distance from. If this is true, then we should see ourselves as more unique from other people who display the negative traits we seek to hide (or even fear) within ourselves.
Jeff Schimel (professor of psychology at The University of Alberta) and colleagues gave people feedback that they were high in anger or low in anger. They then had people rate their own interest in a variety of activities and then rate a different person's interest. They were told that this person scored high on an anger test.
In short, if you were in the study, you would be more likely to rate yourself as unique from the other (angry) person if you had just been told that you were angry, compared to if you had not been told that you were angry. That is, you would distance from the person who has the trait that you do not like, but feel that you yourself have.
A follow up study found this using dishonesty instead of anger.
This is consistent with research showing that people perceive others as more angry when they are perceiving themselves as angry, and in doing so, feel less angry themselves. It also is consistent with research showing that when our self-esteem is threatened or challenged, we tend to degrade other people to make ourselves feel better.