How and why does the ATR-72 sometimes use reverse thrust to push back from its parking position?
As other answers note, for most aircraft, the risk of the engines ingesting FOD while powering back is too high. This is particularly true for turbofan engines mounted under the wings.

Turboprop engines tend to be mounted on high wings (such as on the ATR-72), and they tend to serve smaller airports where an airline may not have tugs available for pushback. Regional and private jets, which often have fuselage-mounted engines, also tend to serve such smaller airports. These planes were designed with the engines mounted higher specifically to reduce the risk of ingesting FOD, thus allowing them to safely power back when needed.

Note that powering back still burns a lot of fuel, and even with high engines the FOD risk isn't zero, so when operating at larger airports that do have tugs available, airlines will generally use them.