Why do we turn it off

Wait until you fill up an airplane. Of course the engine is turned off but the aircraft is grounded with a ground wire to dissipate any static electricity before the gas cap is removed. A running engine does pose a fire hazard in the event of a spill or build up of fumes.

If the gas fumes in the air hit a stoichiometric ratio of between 7% and 15% it becomes explosive, and the spark plugs in your engine could ignite it.

It would take a perfectly windless day for that to happen, but better safe than sorry.

Turning your car off while pumping gas is a safety measure to prevent potential fires or explosions due to static electricity buildup and fuel vapors. While rare, a spark from static electricity could ignite the gasoline vapors, especially when heat from the running engine is present.

Seriously?

All fuel pump nozzles that are inserted into a vehicle's fuel tank are made of aluminum, not steel which reduces the possibility of a static spark from being transmitted from the nozzle to the fuel tank filler hole.

Incorporated into that aluminum nozzle is a grounding wire which is integral with the nozzle and the rubber hose leading to the pump. When the nozzle is inserted into the fuel tank opening, all static electricity contained within the structure of the vehicle is immediately 'grounded' through the aluminum fuel nozzle.

The reason we turn off the car's engine when refueling is because an engine that is running generates static electricity even while it is idling at a stop. Although the car is grounded by the fuel nozzle, a human being is not grounded by that same fuel nozzle because our hand does not touch the aluminum casing of the nozzle, only it's rubber covering. This means our body is not grounded while we're refueling our car.

If the engine is running and is developing static electricity as it idles, as soon as the person refueling the vehicle touches any part of the car while standing on the ground beside the car, a static spark WILL BE created precisely where his hand touches the car.

If the driver got inadvertently splashed with fuel during refueling or any refueling fumes are rising out of the fuel tank during refueling, that static spark created by the idling engine would ignite the fuel on the person or would ignite the fumes in the air surrounding the person who's doing the refueling.

That is also why cellphones cannot be used during refueling. A cellphone is a radio-transmitting device which can ignite fuel vapors during cellphone transmissions including texting, not through a static spark. There is no static electricity generated by a cellphone.

Because BANG

As an explosion preventative

So it doesn't catch on fire and explode?

<------- Knows better. Difficult to hot wire twice.