Basically, it’s the Coriolis effect. It’s what makes “storm systems” in the Northern Hemisphere spin counter-clockwise, and clockwise in the Southern Hemisphere (Mostly, it’s the fact that Northern Hemisphere high pressure areas spin clockwise, leaving the LP areas to spin the opposite of that.). It’s also what makes the Gulf Stream rotate the way it does, too, as well as the North Pacific Gyre.
But with hurricanes, the “movement” of the storm is less predictable, because they follow the low pressure troughs between other systems. Despite how powerful we consider hurricanes to be – and for their size, they sure are! – they are dwarfed in terms of “absolute power” by every single high pressure or low pressure weather system that covers continent-sized swaths of ground. Hurricanes only cover a few hundred square miles, and they are subject to the higher powers contained in “regular” weather systems.