Erebor doesn't care about anybody.
Send me a misconception you think people have about my character and I'll explain if it's true or not
Oooh, I was expecting this one. The fact is that Erebor actually cares too much. She cared about the dwarves enough to let them in her halls, first just to mine, and then to take care of after the fall of Khazad-dûm.
She turned cold after they took the Arkenstone from her halls, after all, those she trusted in there betrayed her in what she saw as the worst way possible. She had already seen what happened to another who had his heart removed, and the wreckage caused by it, after all. There was a reason that people under the thrall of the Arkenstone acted similar to those under the thrall of the One Ring.
If you want to see her caring, go look at how she treats those she has adopted. The twin swords of Fili, the bow of Kili, the sword of Thorin. The young wolf who somehow ended up in Middle Earth. The very volcano that has been her other half since the world was created. The hobbit that somehow was able to ignore the pull of her heart, if only to try to save those he cared about.
If she grows to care for you, she will care for you as long as you give her a reason to. She even cares for some of the dwarves, those who were not originally from her halls to begin with, and if she ever talked to the ones who were, she would probably forgive them.
