This is because you are talking about the movement of a fluid, not a solid. Wind is composed of air, which, like water, is classified as a fluid. Since wind and water are both fluid, they are measured by the same unit.
The old sailing ships used a knotted rope which was being pulled off a spool to determine how fast they were moving through the water. The sailors didn't have any familiar landmarks to sight, so they had to improvise with the materials they had aboard the ship to gauge their speed. Similarly, wind speed doesn't cover ground in the same fashion something like a land vehicle does, such as a truck or car.
An airplane traveling through the wind, with a strong tailwind pushing it along, finds the going easy, actually faster than if the situation were reversed and it was flying into the wind; a headwind would slow the airplane down. This is similar to the way ocean waves speed or slow the motion of ships.
The patterns of winds also pulse, which means the speed is not constant, which would also make it sensible to use knots for speed measurement, not miles per hour, because terrain traveled is constant, not pulsing like wind.
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