Though this is a good observation, Tolkien explains quite a bit of the dwarf/elf animosity right there in The Hobbit: The actual story of this event can be found in The Silmarillion, specifically "Of The Ruin of Doriath." The elf-king Thingol contracts with some dwarves to set a silmaril into a necklace called the nauglimir, which had been made by the dwarves for a fellow elf-king who was now dead. The dwarves try to steal it, claiming ownership, as well as lured by the silmaril, and they assassinate Thingol when he protests. Thus began the hatred between elves and dwarves. When Tolkien wrote The Hobbit, much of the stories that would later be published in The Silmarillion were already extant in one form or another. So he made little connections throughout what was supposed to be a children's story to his greater legendarium, including the way Elrond notes that Gandalf and Thorin's swords once belonged to his great-grandfather Turgon, the elf-king of Gondolin.