What is this whirring noise?
Whirring noise only while decelerating at any or all speeds is most likely caused by bad pinion bearings or loose pinion bearing preload, and almost never by bad ring and pinion gears.

A howl or whine during acceleration over a small or large speed range is usually caused by worn ring and pinion gears or improper gear set up.

Rumbling or whirring at speeds over about 20 mph can be caused by worn carrier bearings. The noise may change while turning.

Regular clunking every few feet may indicate broken ring or pinion gears.

Banging or clunking only on corners can be caused by broken spider gears, lack of sufficient positraction lubrication, or worn positraction clutches.

Rumble while turning may indicate bad wheel bearings.

A steady vibration that increases with the vehicle’s speed can be caused by worn u-joints or an out of balance driveshaft.

Clunking only when starting to move or getting on and off the gas might be loose yokes, bad u-joints or worn transfer case or transmission parts.

When I installed my gear set it was quiet, but it's getting loud with time. What happened?
It is most likely a result of the gear not being broken in properly or driven "too hard, too soon." When this happens, the gear oil breaks down and the resulting temperature inside the differential causes the face of the gear to wear away exposing the softer metal underneath. When this happens the gear will wear down more and more until the gear completely fails.