Fan speed switch: why OFF :: HIGH :: MED :: LOW?

Fans of that type have induction motors with two windings with a capacitor in series with one of the windings. For every individual motor design there is a certain capacitor value that allows the motor to develop maximum torque and operate at the maximum corresponding speed. Smaller capacitor values are used to reduce the torque so that the load overcomes the motor's torque and slows the motor down.

When the motor is turned on, the motor must overcome the static friction of the bearings and get the fan moving. It must then accelerate the motor inertia. That means that using the highest torque setting is desirable for starting the motor. Once the fan is moving, the torque can be reduced for lower speed operation.

It may be intentionally designed to force the fan on "high" for it to spin up before allowing it to drop back down to "low"

The amount of power needed to overcome the static rolling resistance can be higher than what is output to maintain the "low" speed, thus it could end up stalling and not moving or only wiggling back and forth on a "low" setting

Not just fans

A lot of devices are designed this way. It almost seems standard, even though I agree it is counter-intuitive.

For example, in my kitchen I have:

• Cooktop hood fan/light - fan goes from Off to High to Low (continuous except for switch Off)
• Cooktop hood fan/light - light goes from Off to High to Low (discrete settings)
• Cooktop gas burners - Off to High to Low (continuous except for switch Off)

In the case of the fan, the other answers regarding motor startup make sense and would apply to this fan as well.

In the case of the light, I suspect it is to match the fan since it is part of the same device.

In the case of the burners, I think it is because ignition needs to be done when first turning on a burner and ignition is most reliable on the High setting, so starting with High makes sense.

The end result is all using the counter-intuitive Off->High->Low