For a body undergoing pure rotation, its axis of rotation

For a body undergoing pure rotation, the axis of rotation is the line about which all particles of the body revolve in circular paths.

The axis of rotation can be located anywhere depending on the physical constraints.

It can pass through the centre of mass (for example, a uniform disc rotating about its central axis).

It is not necessary for the axis to pass through the centre of mass (for example, a rod pivoted at one end).

The axis can pass through a particle of the body (for example, a solid sphere rotating about its diameter).

It is not necessary for the axis to pass through a particle of the body (for example, a ring rotating about its central axis, where the axis passes through empty space).

Therefore, the axis of rotation can pass through a particle of the body and can pass through the centre of mass.