Hi,
That's a very good question.
In olden days, before the invention of synchro-mesh gears, you'd grind the gears something fierce on down-shifts unless the engine speed and the transmission speeds are substentially similar. When you down-shift, the engine speed tails off (throttle off), but the wheel speed is just a hair less then when you declutch. So if you shift into the lower gear without first raising the engine speed, the speed mis-match will cause a lot of gear grinds and jerky motion. This is exascerbated (sp?) as the lower gear requires an even higher engine speed for the same wheel speed.
In the double-clutch down-shift, you shift into neutral, let the clutch out, blip the throttle to reset the transmission gear speed (they only reset when in neutral and the clutch is out). At the same time, that raises the engine speed such that when you release the cluctch after the down-shift, the engine and the transmission gears are both spinning at similar speed, minimizing gear grind. That's why we call that 'Rev match' -matching the revolutions (engine and wheel).
With the newer manual transmissions, there is something called a synchro gear (or synchro-mesh) in the transmission/clutch assembly. The synchro is a cone-shaped-teeth gear set, so when you let off the clutch, and the engine/transmission come together and re-engage, the cone-shape teeth gearing allows them to slide in place and mesh together (thus synchro-mesh) much easier, with much less grind. So technically, with the newer manual transmissions, you do not have to double clutch, or even rev match, to down-shift, and your clutch/transmission will last a long time.
However, rev match gives you a smooth shift as the engine and transmission are spinning at similar speed, thus no component will drag on the other when they re-engage, producing a jerky clutch engagement.
We enjoy the doube clutch down shifts because the sound of the throttle blip is most heavenly.
Hope this helps a little.
CP