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I think similar questions have already been asked but they are just similar not same.

I completely agree with the fact that product moment of inertia is a physical quantity but i am not able to find a satisfactory(as per me) example which tells the actual reason behind why the mass distribution along y axis will resist rotation about x axis?

Does that mean when a body of arbitrary shape is rotated along y it will soon start having an angular acceleration along x too? I am not able to intuitively feel this. Shouldn't the body rotate normally, with only the mass distribution perpendicular to whatever axis it is rotating, effecting it?

Please correct me wherever i am wrong and suggest examples, links or videos to give it an intuitive feel.

P.S. I actually tried to search a lot before asking here. Any help would be great.

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A simple example:

Imagine a rectangular shape with weights in the top right and bottom left corners. You try spinning it about the long axis. What happens?

enter image description here

The spinning weights will result in a torque; the torque results in precession.

This happens any time you try to rotate about an axis that is not the principal axis of the system. Google "Euler angles" for more about the subject.

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