What is the significance of Mr. Fitweiler's character?

Ulgine Barrows is obviously a monster. One of Thurber's problems in writing "The Catbird Seat" was to make it plausible that the company president Mr. Fitweiler would hire such a woman without knowing anything at all about her. He meets her by accident at a party and almost immediately hires her as his special advisor with unprecedented managerial powers.
In creating the character of Mr. Fitweiler for “The Catbird Seat,” James Thurber had to account for the fact that this president of a large firm would have acted so gullibly in hiring Ulgine Barrows as his special advisor without knowing anything about her qualifications and then supporting her when she began creating chaos within his organization. Throughout the story Thurber emphasizes that Fitweiler is getting old and possibly senile. The author describes him as “the aging gentleman,” “that old windbag,” “the old goat,” and “the old buzzard.” When Ulgine Barrows realizes she has been double-crossed by Martin, she completes her own destruction by shouting at Fitweiler, “Can’t you see how he has tricked us, you old fool?”
It is Fitweiler’s age and mental decline that explain why he hired Ulgine Barrows in the first place and then why he could not see that she was incompetent and destructive. His old age, which is subtly emphasized in various ways, also explains why he is taken in so easily by Martin’s plot. Martin understands his boss better than his boss understands himself. When Fitweiler explains why he is discharging his special assistant, he reveals that he has a psychiatrist named Dr. Fitch. No doubt he has been seeing a psychiatrist because he has been suffering from some sort of mental ailments, such as Alzheimer’s disease, connected with aging. He has just consulted Dr. Fitch about Ulgine Barrows on the telephone and had his own assessment of her substantiated by his psychiatrist. Fitweiler has picked up a lot of psychiatric jargon from Dr. Fitch. He explains the following:
“It grieves me to report that she has suffered a severe breakdown. It has taken the form of a persecution complex accompanied by distressing hallucinations.”
Thurber was the first prominent American humorist to incorporate neurosis and psychosis into his stories, essays, and cartoons, as can also be seen in his best-known story, “The Secret Life of Walter Mitty.” Since Thurber's time, psychological humor has become a staple of humor and comedy.