**Core Concept**
Autoimmune thyroiditis, a condition where the immune system attacks the thyroid gland, often co-exists with other autoimmune disorders due to the shared genetic predisposition and environmental triggers. This phenomenon is known as autoimmune polyendocrine syndrome.

**Why the Correct Answer is Right**
Psoriasis, a chronic inflammatory skin condition, is primarily an autoimmune disease caused by an inappropriate immune response against the skin cells. Although it shares some genetic and environmental factors with autoimmune thyroiditis, it is not typically classified as an autoimmune endocrine disorder. In contrast, conditions like myasthenia gravis (B), an autoimmune neuromuscular disorder, and type 1 diabetes mellitus (A), an autoimmune pancreatic disorder, often co-exist with autoimmune thyroiditis.

**Why Each Wrong Option is Incorrect**
**Option A:** Type 1 diabetes mellitus is an autoimmune disorder that frequently co-exists with autoimmune thyroiditis, highlighting the shared underlying pathophysiology.
**Option B:** Myasthenia gravis is an autoimmune disease that often co-exists with autoimmune thyroiditis, due to the shared genetic predisposition and environmental triggers.
**Option C:** There is no direct association between Sly syndrome (Mucopolysaccharidosis type VII) and autoimmune thyroiditis; however, this option is not directly related to the question.

**Clinical Pearl / High-Yield Fact**
Autoimmune thyroiditis often co-exists with other autoimmune endocrine disorders, such as type 1 diabetes mellitus, Addison's disease, and hypoparathyroidism, due to the shared underlying pathophysiology and genetic predisposition.

**✓ Correct Answer: D. Psoriasis**