Final answer:
Multiple sclerosis (MS) is the autoimmune disease that leads to the damage of myelin sheaths in the central nervous system, resulting in a range of neurological symptoms and impairment.
Step-by-step explanation:
The autoimmune disease that causes progressive inflammation and deterioration of the myelin sheath is Multiple sclerosis (MS). MS is a central nervous system disease characterized by the immune system mistakenly attacking the protective myelin sheaths around nerve fibers, which leads to scarring (sclerosis) and a range of neurological symptoms. These symptoms include visual disturbances, muscle weakness, difficulty with coordination and balance, sensory changes like numbness, and cognitive impairments. The progressive damage to myelin affects the transmission of electrical signals in the nervous system, severely impacting motor and sensory functions.