The Ziehl-Neelsen stain is specifically designed to detect acid-fast bacilli like Mycobacterium tuberculosis because their cell walls contain mycolic acid, which retains the red dye even after acid-alcohol decolorization. This property is unique to mycobacteria, making Ziehl-Neelsen the gold standard for identifying tuberculosis in sputum samples. Other stains, such as Gram stain, do not reliably highlight these organisms due to their waxy cell envelope.

Reference:
Jawetz, Melnick & Adelberg's Medical Microbiology, 27th Edition, Chapter on Mycobacteria/Tuberculosis, Page 250.