In order to answer this question, we need to go back two generations. Georg and Ulrich hated each other, but the animosity started with their grandfathers. According to the story, there was a small tract of land that was disputed between the Gradwitz and Znaeym families. The courts ruled in favor of the Gradwitz family (wealthy landowners) against the Znaeym family (petty landowners).
Needless to say the court ruling did not resolve anything, because the Znaeym family did not accept the court ruling. Moreover, Ulrich and Georg hated each other, not only on account of the family feud, but also because there was personal hostility. Both men took the present state of affair personally to the point of wanting to kill each other. Here is what the text says:
The forest lands of Gradwitz were of wide extent and well stocked with game; the narrow strip of precipitous woodland that lay on its outskirt was not remarkable for the game it harboured or the shooting it afforded, but it was the most jealously guarded of all its owner's territorial possessions. A famous law suit, in the days of his grandfather, had wrested it from the illegal possession of a neighbouring family of petty landowners; the dispossessed party had never acquiesced in the judgment of the Courts, and a long series of poaching affrays and similar scandals had embittered the relationships between the families for three generations. The neighbour feud had grown into a personal one since Ulrich had come to be head of his family; if there was a man in the world whom he detested and wished ill to it was Georg Znaeym, the inheritor of the quarrel and the tireless game-snatcher and raider of the disputed border-forest.