One - Literally streets that the couple walked upon, filled with memories, until they argued there and "stained these walls With our mistakes and flaws". In the argument, the guy was wrong, or sad something, and he regrets it, because "These streets are yours, you can keep them, I don't want them. They pull me back, and I surrender To the memories I run from." He's running away from the memories almost with his tail between his legs, "I won't show my face here anymore" because he's embarrassed, ashamed, of what he's done.
Or two - 'These streets' are a metaphor for all their memories together. Again, he made such a mistake that he doesn't want to remember any of them, "All that's left behind Is a shadow on my mind" - he trying to forget the memories, or repress them.
Either he hurt her, or they mutually departed from a destructive relationship, or she hurt him. Either way it was messy and painful, and he doesn't want to remember the time the had together.
To me, this song could be one of two things.
One - Literally streets that the couple walked upon, filled with memories, until they argued there and "stained these walls With our mistakes and flaws". In the argument, the guy was wrong, or sad something, and he regrets it, because "These streets are yours, you can keep them, I don't want them. They pull me back, and I surrender To the memories I run from." He's running away from the memories almost with his tail between his legs, "I won't show my face here anymore" because he's embarrassed, ashamed, of what he's done.
Or two - 'These streets' are a metaphor for all their memories together. Again, he made such a mistake that he doesn't want to remember any of them, "All that's left behind Is a shadow on my mind" - he trying to forget the memories, or repress them.
Either he hurt her, or they mutually departed from a destructive relationship, or she hurt him. Either way it was messy and painful, and he doesn't want to remember the time the had together.