The Jackass Syndrome
Some years ago, I watched an episode of the show Just Shoot Me! where one of characters used the phrase "The Jackass Syndrome" to describe the situation were two people who are quite similar in some ways can really hate each other (it was followed by a short scene in which, after two people met for the first time, each of them walked away muttering "jackass" in reference to the other person).
Over the years I have noticed that sometimes people that are indeed similar in some aspects (that they may not be aware of) can not get along with one another. Is there another word for this situation?
Solution 1:
There are phrases relevant to the phenomenon, but I'm not familiar with any single word.
We hate most in others what we fear most in ourselves.*
and
The pot calling the kettle black
are both applicable in situations wherein one person finds objectionable in another an attribute that s/he, too, possesses.
The psychological concept of projection is not unrelated. People who project generally deny feelings or desires within themselves and ascribe them to others.
*Rather than fear most, you might also hear see or even can't see.