The story shows a very frustrated and frazzled Mr. Martin who wants to get rid of Mrs. Barrows.  At first, he actually contemplates killing her.  The reader is unaware, in fact, that he is not still going with that plan when he goes to her apartment.  The structure of not letting the reader in on all the details of the plan are part of what keep the reader interested.  Also, Thurber writes with great detail giving the reader a vivid description of Mrs. Barrow's voice and mannerisms so that the reader finds them as detestable as does Mr. Martin.  The tension builds when Mr. Martin goes to Mrs. Barrow's apartment and makes outrageous and preposterous claims about drug use and such.  It's clear that this gives Mrs. Barrows all she needs to get rid of him.  She simply has to report his behavior to the boss which she does the next morning at work.  The reader expects Mr. Martin to be fired immediately, but he simply denies everything and since he is such a creature of habit and he is so meek and mild-mannered, no one believes anything she says.  She is the one that gets removed from the office, not Mr. Martin, thus allowing him the victory he sought.