Paul's father is crucial to the the overall meaning (the theme). Paul's father represents everything that Paul despises about his existence: the hardworking "American Dream," the hum-drum monotony of the town he lives in, and the oppressive nature of expectations that Paul does not want to live up to. His father ignores Paul's desire to become a performer, and Paul feels he is constantly being admonished and punished. It is because of these things that Paul has had enough and resorts to stealing money from his employer and running off to New York. In addition, eNotes states:
To Paul...his father represents oppressive authority and the dreary middle-class life of Cordelia Street. He dreads coming home late to his father, "the figure at the top of the stairs," with his "inquiries and reproaches."