Here's why:

* Acid-fast bacteria have a waxy cell wall that is resistant to decolorization by acids.

* Acid alcohol is a mixture of a weak acid (typically hydrochloric acid) and alcohol.

* The acid helps to break down the waxy layer, but it doesn't completely remove the dye.

* The alcohol helps to remove any excess dye that is not bound to the waxy layer.

This means that only acid-fast bacteria will retain the primary stain (carbolfuchsin) after the decolorization step. Non-acid-fast bacteria will lose the stain and be counterstained with a different color.

Important note: Some variations of the acid-fast stain might use different decolorizing agents, but the principle remains the same: to remove the primary stain from non-acid-fast bacteria while preserving it in the acid-fast ones.