Why exactly should Hurricane be distributed to only flying-types? The logic behind Pokemon can be easily based on that they are able to whip up large gusts and winds, in case of Shiftry which it can use it's fans like hands to do so.
Shiftry is a mysterious Pokémon that is said to live atop towering trees dating back over a thousand years. It creates terrific windstorms with the fans it holds.
Shiftry's large fans generate awesome gusts of wind at a speed close to 100 feet per second. The whipped-up wind blows anything away. This Pokémon chooses to live quietly deep in forests.
—Ruby and Sapphire entry for Shiftry
This is probably why it's able to learn Hurricane.
Hope this helps!