Hermione supports her point of view by emphasizing the importance of studying for their exams, which she believes are critical for progressing to their second year at Hogwarts. She argues that the exams are approaching quickly, citing the ten-week timeframe as something significant rather than remote, comparing it to "like a second to Nicolas Flamel," someone who is centuries old. This comparison underscores her perception of time and urgency regarding the exams.
Additionally, Hermione points out that she feels unprepared and expresses her frustration over her companions' lackadaisical attitude towards studying. By stating, "I should have started studying a month ago," she demonstrates that she takes her academic responsibilities seriously and feels the pressure to perform well. Her structured approach to studying, with the creation of study schedules and color-coded notes, contrasts with Harry and Ron's more relaxed attitude, further highlighting her commitment to her education.