The Notebook

At a modern-day nursing home, an elderly man, Duke, reads a romantic story from his notebook to a fellow patient.
In 1940s Seabrook Island, South Carolina, Noah Calhoun is smitten with seventeen-year-old heiress Allie Hamilton after seeing her at a carnival, and they have a summer love affair. Noah takes Allie to an abandoned house that he intends to buy for them. They try to make love, but are interrupted by Noah's friend Fin with the news that Allie's parents have the police looking for her.
When Allie and Noah return to her parents' mansion, Allie's mother Ann calls Noah trash and they ban her from seeing Noah. Noah walks out and Allie chases after him. The ensuing argument between the two ends in a break up and the next morning, Ann announces that the family is returning home to Charleston. Allie attempts to contact Noah, but is unable to find him, so she asks Fin to tell Noah that she loves him. When Noah gets the message, he rushes to Allie's home only to find the house empty.
Noah writes to Allie every day for a year but Allie's mother intercepts the letters and they never reach Allie. Noah enlists with Fin to fight in World War II, where Fin is killed in battle. Allie volunteers in a hospital for wounded soldiers, where she meets officer Lon Hammond, Jr., a young lawyer who comes from old Southern money. The two become engaged, to the delight of Allie's parents.
When Noah returns home from the war, his father has sold their home so that Noah could buy the abandoned house. While visiting Charleston, Noah witnesses Allie and Lon kissing at a restaurant; he convinces himself that if he restores the house, Allie will come back to him. Allie is startled to read in the newspaper that Noah has completed the house to the specifications she'd made years prior, and visits him in Seabrook.
Allie returns to Seabrook to find Noah living in the restored house. The two renew their relationship and make love. In the morning, Ann appears on Noah's doorstep, warning Allie that Lon has followed her to Seabrook. Ann reveals that in her youth she had been in love with a lower class young man and still thinks of him. She then gives Allie the letters that Noah had written to her, admitting that she had hidden them from Allie. Allie confesses to Lon that she has been spending time with Noah. Allie tells Lon she knows she should be with him, but she remains indecisive.
In the present, it is revealed that the elderly woman is Allie, who is suffering from dementia. Duke is actually Noah, who is her husband, but Allie does not recognize him, nor remember any of the events Noah is reading to her. Allie briefly becomes lucid. She remembers that the story Duke is reading is the story of how they met. Duke tells her how she appeared at Noah's doorstep with her belongings, having left Lon at the hotel, and Allie suddenly remembers her past. At the onset of her dementia, she wrote their love story in the notebook with instructions for Noah to "read this to me, and I'll come back to you." But Allie soon relapses, losing her memories of Noah. She panics, not understanding who he is, and has to be sedated. Duke, who is in fact Noah, is hospitalized with what seems to be a heart attack.
When he is released from the hospital, Noah visits Allie and finds her lucid again. Allie is scared of her dementia and asked what Noah would do should she lose her memories forever. Noah reassures her that he will never leave her even if she was to succumb to dementia, replying that their love can do anything. After each tells the other that they love them, they both go to sleep in Allie's bed. The next morning a nurse finds that they have died peacefully in bed together.

Question: Why did Fin interrupt?
Answer: Fin wanted to tell Noah and Allie her parents had the police looking for her.