You may have noticed that the eNotes editors who originally wrote the summary guides for James Thurber's "The Catbird Seat" gave two different thematic outlines for the story: "Men and Women" and "Alienation and Loneliness." I think they are good summaries.
MEN AND WOMEN. Many of Thurber's stories have to do with life's little battles between men and women ("The Secret Life of Walter Mitty," for example). Such is the case with "The Catbird Seat." Perhaps a secondary theme would be that of role reversal. Mr. Martin and Mrs. Barrows are drawn by Thurber with their typical male-female roles reversed: Mrs. Barrows is the loud, sports-loving boss; Martin is the quiet, milk-drinking office subordinate. When she makes accusations against Martin, they are discounted because his milquetoast personality and routines make the charges against him impossible to believe. In this story, Thurber's male character triumphs against female authority--not always the case in Thurber's literary world.
ALIENATION AND LONELINESS. Like many of Thurber's characters, both Martin and Barrows have trouble dealing with other people. Both live alone and each seem to prefer it that way. Their limited social lives revolve around work hours, and Martin is barely noticed after more than two decades with the company. However, he is content with his near anonymity. When Barrows advances quickly, Martin becomes jealous. Her masculine nature angers him, and he hates that she stands out because of her more outgoing personality. After she is gone, Martin summises, he can return to his quiet ways and peaceful work days.