**Core Concept**
Frederich's ataxia is an autosomal recessive inherited disorder characterized by progressive damage to the nervous system, particularly the cerebellum and spinal cord. It is caused by an expansion of a GAA repeat in the FXN gene, leading to a deficiency of the mitochondrial protein frataxin.

**Why the Correct Answer is Right**
The correct answer is related to the pathophysiology of Frederich's ataxia. The disease is caused by a deficiency of frataxin, which plays a crucial role in maintaining mitochondrial function and iron homeostasis. The lack of frataxin leads to mitochondrial dysfunction, oxidative stress, and iron accumulation, ultimately resulting in the degeneration of neurons in the cerebellum and spinal cord.

**Why Each Wrong Option is Incorrect**
* **Option A:** Frederich's ataxia is indeed an autosomal recessive disorder, so this option is incorrect.
* **Option B:** Frederich's ataxia is characterized by progressive damage to the nervous system, particularly the cerebellum and spinal cord, making this option correct.
* **Option C:** Frederich's ataxia is indeed caused by an expansion of a GAA repeat in the FXN gene, so this option is incorrect.
* **Option D:** Frederich's ataxia is characterized by a deficiency of frataxin, which plays a crucial role in maintaining mitochondrial function and iron homeostasis, making this option correct.

**Clinical Pearl / High-Yield Fact**
Frederich's ataxia is a classic example of a genetic disorder that is caused by an expansion of a trinucleotide repeat in a gene. This type of mutation is known as a trinucleotide repeat disorder, and it is responsible for several other neurodegenerative diseases, including Huntington's disease and spinocerebellar ataxia.

**Correct Answer:** C.