Must have been bored on way home from work, was thinking about this peculiar question. One of those that, if you need to ask, you'll struggle with the explanation.
Or perhaps it is the other way around: try this yourself at a track, and you will quickly have the answer with no further words needed.
Anyway, riding home and was going down a few gears for a red light and was reminded that a motorcycle gearbox cannot be relied upon even to change down several gears reliably with the clutch "in". You need the clutch to transmit chain pull from the rear wheel and move the shift dogs a bit or one of your successive prods on the lever might not make a shift.
So that alone is a reason why releasing the clutch a bit while downshifting helps.
The other of course is that at corner apex on the track you are aiming to be going so fast that the tyres are using all their grip just to support you at lean. Idea is you then open the throttle a smidge at first and that is enough to begin a very gentle rear-tyre drift if you get it (i.e. your apex speed) just right.
Obviously trying to do all that while simultaneously releasing the clutch after a multiple downchange adds enormously to the difficulty.
Go slow enough and sure, you will manage it easily.