Common sense + Experience...
The purpose of clutch is to disconnect the engine from gear box..... When the clutch is released, even in neutral, the two wheels (girariyan) are engaged and when u press the clutch, they dis-engage from each other making smooth way for the gear to be engaged. When the gear is applied and you release the clutch, the both wheels again engage with each other.
Now wheel always runs on ball bearing.... There is a ball bearing which may have some play in it.... When u press the clutch, they dis-engage and due to which one wheel of them that is connected to clutch stops rotating, no rotation so no play and no play so no noise. But when u release the clutch, both wheels pack together and the wheel in the engine which is already rotating, make the other wheel rotate which is having play in it.... So rotation leads to occur that play and that bearing starts screaming again......