In "The Catbird Seat," what was the main reason Mr. Martin wanted to kill Mrs. Barrows?

Mr. Fitweiler hired Mrs. Barrows at his special assistant without knowing anything about her. Fitweiler, who is head of the big New York-based F&S company, is getting old and seems to be gradually losing his mind. He is going to a psychiatrist for help. His hiring Ulgine Barrows as his assistant was obviously a big mistake. Mr. Martin reflects:

A week later he had introduced her as his special adviser. On that day confusion got its foot in the door.

She has created disruption throughout the executive offices by her reorganization schemes. In order to show her irrationality, the narrator keeps quoting the "gibberish" Mrs. Barrows is always spouting . She repeats phrases she has heard on the radio spoken by a popular baseball sportscaster named Red Barber. They include the following:

"Are you lifting the oxcart out of the ditch? Are you tearing up the pea patch? Are you hollering down the rain barrel?: Are you scraping around the bottom of the pickle barrel? Are you sitting in the catbird seat?"

"Sitting in the catbird seat" meant "sitting pretty, like a batter with three balls and no strikes on him." Ulgine Barrows has been driving Martin crazy with these mindless questions. She seems to be trying to learn to be "one of the boys" in an era in which women were entering the American workforce in large numbers and moving up to positions of power. But Martin treats her with friendly tolerance until it appears that she has her eye on his filing department. On the afternoon of Monday, November 2, 1941 she had bounced into Mr. Martin's office and asked, "Do you really need all these filing cabinets?"

Mr. Martin could no longer doubt that the finger was on his beloved department. 

He addresses an imaginary jury in his head:

"Gentlemen of the jury," he said to himself, "I demand the death penalty for this horrible person."

The reader expects to be reading a perfect-crime murder story; but Mr. Martin eventually thinks of a more subtle way of getting rid of Mrs. Barrows. Mr. Fitweileer discharges her because she thinks the staid and loyal company man Mr. Martin could have said and done the things of which she accuses him, including getting "coked to the gills" on heroin, and therefore the woman must be mad. It turns out that Mr. Martin was correct in foreseeing that, "Her pickaxe was on the upswing, poised for the first blow." After Mrs. Barrows is dragged forcefully out of Mr. Fitweiler's office, he tells Martin:

"You may not know, Martin, but Mrs. Barrows had planned a reorganization of your department--subject to my approval, of course, subject to my approval. This brought you, rather than anyone else, to her mind--but again that is a phenomenon for Dr. Fitch and not for us."