It's funny because the metaphors in the song are so bad, but it's somehow so good. They keep changing what the diamond is a metaphor for.
1) the diamond is the narrator's heart that the SO stole and the narrator wants back
2) the diamond is the relationship that seems more valuable than it is
3) stealing diamonds is something unhealthy the people in the relationship do ("you tell me not to steal, yet you still want a thief"--they encourage each other's bad behavior)
4) the diamond is the narrator, who the SO wants to change ("cut") instead of accepting her for who she really is
It's funny because the metaphors in the song are so bad, but it's somehow so good. They keep changing what the diamond is a metaphor for. 1) the diamond is the narrator's heart that the SO stole and the narrator wants back 2) the diamond is the relationship that seems more valuable than it is 3) stealing diamonds is something unhealthy the people in the relationship do ("you tell me not to steal, yet you still want a thief"--they encourage each other's bad behavior) 4) the diamond is the narrator, who the SO wants to change ("cut") instead of accepting her for who she really is