Ulgine Barrows has many unpeasant character traits. Mr. Martin is not the only one in the firm who dislikes her. The company president Mr. Fitweiler seems to be the only one who likes her and considers her an asset to his company. Thurber contrasts her with Mr. Martin. She makes him seem exceptionally quiet, modest, meticulous, and serious, while he makes her seem loud, rude, aggressive, ignorant, and vulgar. In Jungian terms, Mr. Martin is an extreme introvert (not unlike Herman Melville's Bartleby the scrivener), while Ulgine Barrows is an extreme extrovert. It is only because Mr. Fitweiler is getting old and somewhat senile, as well as the fact that he is having to see a psychiatrist, that he would have done such a reckless and unorthodox  thing as to employ an inexperienced and unqualified person like Ulgine Barrows as his special adviser and let her create chaos in his firm. The fact that she keeps repeating sayings she has picked up from a radio baseball announcer is used to highlight her level of mentality. It is because of her vulgar mentality that she fails to sense the subtlety of Martin's plot--but at least she doesn't get murdered as he originally planned.