this is a dogs instinct and is all about resources,by chasing away cats the dog will have accsess to more prey to sustain itself and its pack.
a pack of dogs will chase away other dogs too for the same reason.
it is the same with foxes dogs will chase them.
foxes will try to chase away cats too even if they have limited sucsess against an adult cat.
and as you know cats chase away other cats to avoid competition over the same resources.
if a dog try to chase away a cat but the cat refuses to move the dog will often witdraw from a potential fight(take a look on youtube bad ass cats and you will understand what i mean).
every predatory animal have this instinct to remove competition both pack animals and the solitary ones,lions packs chase away the young males and keep the females(they do most of the hunting)so it makes sense to have them in the pack.