[Orcrist]

Actually, the feud started when Aule, one of the Valar, made the Dwarves without telling Iluvatar. Iluvatar says,"...and often strife shall arise between thine and mine, the children of my adoption and the children of my choice." His children are the Elves and Men. He never intended to make Dwarves. That is why they are the children of his adoption. Anyway, I think that is the main reason for the feud.