What is incongruous about Mr. Martin's boasts to Mrs. Barrows?

The whole plot of "The Catbird Seat" hinges on the incongruity between Mr. Martin's character and his boasts to Mrs. Barrows when he comes to her apartment. He is in reality a very conservative, quiet, thoughtful, studious, mild-mannered man whose job as head of a filing department seems suitable to his inhibited personality. Ulgine Barrows is astonished by his behavior. He asks for a Scotch-and-soda and lights a cigarette.

"Well," she said, handing him his...

The whole plot of "The Catbird Seat" hinges on the incongruity between Mr. Martin's character and his boasts to Mrs. Barrows when he comes to her apartment. He is in reality a very conservative, quiet, thoughtful, studious, mild-mannered man whose job as head of a filing department seems suitable to his inhibited personality. Ulgine Barrows is astonished by his behavior. He asks for a Scotch-and-soda and lights a cigarette.

"Well," she said, handing him his drink, "this is perfectly marvelous. You with a drink and a cigarette."

Mr. Martin had come there with the intention of murdering the woman, but he realizes the incongruity himself and decides to exaggerate it. 

"Here's nuts to that old windbag, Fitweiler," he said, and gulped again.

He tells her he takes heroin and that he will be "coked to the gills" when he bumps the old buzzard off. Ironically, bizarre behavior brings out the conservative side of Ulgine Barrows' character. She is amazed, indignant, defensive of their employer. She soon asks Martin to leave.

"Not a word about this," he said, and laid an index finger against his lips.

As expected, Mrs. Barrows comes charging into the office the next morning and has a long talk with Mr. Fitweiler. She doesn't realize that she has been tricked by Mr. Martin's performance and that he is in the catbird seat. Mrs. Barrows only reinforces Mr. Fitweiler's impression that she has lost her mind when she becomes hysterical. She brings about her own downfall when she glares at her employer and asks: 

"Can't you see how he has tricked us, you old fool? Can't you see his little game?"