I realize, that doors aren't symbolic.
I've made a lot of similar realizations-- windows aren't escapes, the ocean isn't freedom, and roses are a flower, not a floral representation of love.
Closing the door behind you is not saying goodbye. It's keeping the cold air outside out and the hollowing heartbreak in, behind, with me.
So maybe I can't let go of symbolism.
But isn't some kind of semblance of a poem better then what it really is?

The door closing behind you?
Isn't anything better then that?