Molly and Gabriel disagree about the proper relationship to Irish literature and culture. Molly emphasizes knowing Irish language, literature, culture, and even landscape; Gabriel thinks it is important to know the other (larger?) European traditions, and says that he is sick of his country (which is Ireland).
Molly whispers "West Briton" in his ear, which is an insult. It means he supports British rule over Ireland, and implies he is less Irish than she is. She then drives this home by saying an Irish good-bye.