You can find the answer to this question by reading to the end of the story. Just before the end of the story, we find out that "Terry O'Sullivan" is really not an Irishman at all. Instead, he is an Italian whose real name is Tony Spinelli.
Maggie Toole has been unable all these years to get a guy to like her and bring her to the dances. So she has somehow managed to get this Spinelli guy to come with her and has pretended he is Irish. She only reveals what is going on when she finds out that Spinelli is going to fight with Dempsey Donovan.