The word "sentimental" is in the opening line, and that's a good word for this whole song.
It starts off obliquely, the way a person with an embarrassing condition might approach a doctor: "If I had... a friend... who has a rash..."
Similarly, this story starts: "There's a sentimental story/ Of two people that I know..."
It's not really a spoiler, even, to reveal the ending: "I'm the boy-- the girl is you."
Still, the speaker approaches her with this sideways shpiel, telling her about this hypothetical couple who "always loved each other so." In fact, "The people in the story/ Lived a storybook romance."
Well, as the Yiddish saying goes-- if it doesn't get better, it gets worse. Either he is working his way up to a proposal, with something like, "Would you like to live happily ever after with me?
"Then they had a lovers' quarrel/ No, I don't recall the reason why.../ And the boy said, 'Goodbye.'"
He was so mad he broke up with her, and now he doesn't even know what he was mad about. Oops.
But wait, if he broke it off, why is he talking to her now? "Now, he's begging for forgiveness/ And a chance to start anew."
It is an interesting approach:. "Imagine, hypothetically, two people in love, and, in theory, the boy stormed off for no real good reason. If he said he was really really really sorry, hypothetically, she'd have to take him back, right?"
He'd better have a better strategy than this. Let's hope he showed up not just with a "sentimental" song but flowers or chocolates or concert tickets (all they have done so far is "go to movies" and out to "dance").
The good news, he is admitting fault, he is coming forward, and he is not blaming any of it on her. Guys like that don't fall out of the sky. She should tell him they can start a new chapter (oh, great. Now I'm doing it).
Next Song: That Forever Kind of Love