Here's why:

* Gram staining is a technique that differentiates bacteria based on their cell wall structure.

* Acid-fast bacteria have a unique cell wall structure with a high lipid content (mycolic acid). This makes them resistant to decolorization with acid alcohol, hence the name "acid-fast".

* Non-acid-fast bacteria do not have this high lipid content in their cell wall. Therefore, they are decolorized by acid alcohol during the Gram staining process.

* Gram-positive bacteria have a thick peptidoglycan layer in their cell wall, which retains the crystal violet dye during the staining process.

* Gram-negative bacteria have a thinner peptidoglycan layer and an outer membrane. They lose the crystal violet dye during the decolorization step and are counterstained with safranin.

In summary: Non-acid-fast bacteria can be either gram-positive or gram-negative, depending on their cell wall structure. Acid-fastness is a separate characteristic related to the presence of mycolic acid, which is not relevant to the Gram staining classification.