[CaptainSlow]

As you disengage the clutch, the flywheel will be spinning at engine RPM, and the clutch will be spinning proportional to the wheel speed (depending on what gear you're in). Going from a higher gear (fewer rotations of the clutch for every rotation of the tires) to a lower gear (more rotations of the clutch for every rotation of the tires) can put stress on the clutch because it's going from a slower speed to a much faster speed very suddenly. This can build up friction heat, scar the flywheel, strain the springs in the clutch, etc....just puts excess stress on the whole system. If you rev match it's a bit better because you're basically increasing the revolutions of the engine to match the revolutions that the clutch will be spinning at once that lower gear is engaged (clutch released).