So, I'm just gonna take a shot in the dark. The way I hear this song, and I admit it might be jaded by my own experiences, it sounds to me like she was the "other woman" in a relationship with a guy, and it never evolved into anything. This is her plea to acknowledge that not only did he cheat on his other girlfriend, and effect every relationship they'll be in for a while, but that he also did something to Julia. Something just as significant. And all she wants from him is for him to say "I'm sorry for how I hurt you". But clearly, he "cares more that she knows what you did than [he does] that [he] did it to" her.
So, I'm just gonna take a shot in the dark. The way I hear this song, and I admit it might be jaded by my own experiences, it sounds to me like she was the "other woman" in a relationship with a guy, and it never evolved into anything. This is her plea to acknowledge that not only did he cheat on his other girlfriend, and effect every relationship they'll be in for a while, but that he also did something to Julia. Something just as significant. And all she wants from him is for him to say "I'm sorry for how I hurt you". But clearly, he "cares more that she knows what you did than [he does] that [he] did it to" her.
I'm probably wrong tho. so goes.