[Kalimac]

Of course, if you want to go right back to the beginning, it's a cosmic case of sibling rivalry. The Dwarves were created by Aule, who was in such a hurry to see what the children of Iluvatar would be like that he decided to make some himself; Iluvatar was angry at his presumption and though he decreed that the Dwarves should be allowed to live, that they should sleep under the earth for a while, since Iluvatar did not want these interlopers coming before the Elves whom he had intended as firstborn. Iluvatar tells Aule "But when the time comes I will awaken them [the Dwarves] and they shall be to thee as children; and often strife shall arise between thine and mine, children of my adoption and the children of my choice."

With a divine/parental sendoff like that, it's no wonder the Dwarves were a little touchy about the Elves - and vice versa, of course.