It's a fine line to tread, writing a song about someone you'd rather forget. You gotta hit the right notes of anger, regret, carelessness, and above all, apathy. T-swizzle tried to strike that note first with "I forgot you existed". That song was flawed from its conception - if she'd really forgotten, there wouldn't be a song about it, would it? In IFYE, she sings that "something happened one magical night - I forgot that you existed," enabling her to slide into a state of cheerful "just indifference."  I appreciate the effort but if someone'd really forgotten someone else existed so easily, they wouldn't have written a song about it. 

The follow-up effort - "Closure" - works because it doesn't pretend that the process of forgetting is easy, or even possible. "It's been a long time, and seeing the shape of your name still spells out pain" acknowledges right off the bat that the narrator still struggles with the events of the past. But it's not treated as something to be ashamed of, as the narrator immediately asserts afterwards that "It wasn't right - the way that it all went down." It's a stronger asseveration than all the examples that are provided in IFYE. The details of their past relationship are too painful to recall. The listener can take their word for it or not - it does not matter to the narrator. And it's not the point of the song. 

When the narrator receives a letter, they find the energy to respond - "Yes, I'm doing better, it cut deep to know ya... I know that it's over" - before rejecting the sentiment of the letter in disgust. The narrator would rather forget about the entire relationship, and so does the letter writer. but only to ensure that it doesn't inconvenience the letter-writer in the future. The letter-writer treats the narrator "like some situation that needs to be handled... a wrinkle in your new life."  But that pain is part of the narrator's past. And the narrator is surviving with that, singing "I'm fine with my spite, and my tears, and my beers and my candles." Nobody but the narrator can dictate whether to feel shame, how fast to move on, or how to grieve. Even if it was in the distant past.  

And that's important, because sometimes ya don't get to forget the people who hurt you. Workplace broad-spectrum bigots, assaulters, friends who let you down when you really needed them. There's hardly ever any closure. But that's fine - I don't need it from them anymore.