The danger is the debt-deflation spiral: falling prices raise the real burden of fixed nominal debt, borrowers cut spending to service it, demand falls further, and prices fall again. Because nominal rates cannot go far below zero, the central bank loses its main tool exactly when it needs it.
This asymmetry is why targets are set at 2% rather than 0%. The buffer exists so a normal recession does not push inflation below zero, and it is why quantitative-easing and negative-interest-rates were invented.
Example: prices fall 2% a year and the policy rate is at zero. The real-interest-rate is plus 2% and rising, meaning policy is tightening automatically at the worst possible moment.
Related: disinflation, negative-interest-rates, quantitative-easing, real-interest-rate, recession