Why do falling objects make a whistle sound?

Friction

Air friction is the cause of a number of physical effects initiated by a falling object. It will rapidly slow down the moving mass and convert its decelerated motion into other modes. As a function of its velocityIt the object will heat up, light up and emit a high pitch sound (not to be confused with the sonic boom).

Just as the wind can howl about King Lear, because of whatever firm objects the play director may decide to place around him, do make a hissing sound.

In the case of Lear, the air blows through trees or cheminey tops. In the case in point, it is your falling object that moves through the stable air. The result (mutatis mutandis) is the same.