The technical explanation of this truth:

If you are trying to negate the speed of your fall by jumping upwards, it just won't work. In free fall, you fall 5 meters the first second. By the end of the first second, you're falling at 10 meters per second, but you have only fallen 5 meters. At the end of the second second you have fallen 20 meters, and at the end of the third you'll have dropped 45 meters. The distance in meters goes as 5 x time². Now, friction and air resistance will eventually stop the downward acceleration. A human freely falling tends to peak at about 180 kilometers per hour, or about 50 meters a second. That's fast, about twice as fast as a car on a highway. An elevator might do more in a big high rise.

The simple explanation:

You are falling at the same speed the elevator is falling. Any height you gain from jumping at the end of the fall will gain you mere milliseconds and will reduce your speed by almost nothing. Even if you could jump high enough to stop your fall significantly, you would bang your head on the ceiling of the elevator and probably be worse off...