The great-grandfather of the current generation of Beagle Boys, Great-Grandpappy Beagle opposed Scrooge McDuck when the tycoon first settled in Duckburg, as the Beagles had thus far been in charge of the small town and could not bear to see it grow beyond what they could control. Scrooge McDuck's ownership of the deed to Duckburg remained a sore spot between Scrooge and the Beagles ever since, dwarfing any interest the Beagles might have in stealing Scrooge's fortune, and a painting featuring Scrooge getting the deed in front of a powerless Grandpappy still hangs in the lobby of McDuck Manor.
Behind the scenes
His (and, by extension, the other Beagles') storyline appears to be inspired by the 1975 comic story The Deep Sea Deed, which also saw Great-Grandpappy Beagle spurring his descendants to chase after a hallowed deed in Scrooge's possession which had once been the Beagles' ancestor's, although in this case it was a deed giving its holder ownership of all the water in the world. Blackheart Beagle's protests in Don Rosa's A Little Something Special about how before Scrooge came and gave Duckburg an economic boost, he and his Beagles were basically running the town, also likely played a part.