**Core Concept**
Riedel's thyroiditis is a rare form of thyroiditis characterized by a fibrotic replacement of the thyroid gland, leading to a woody, non-tender mass that can mimic thyroid carcinoma. This condition is often associated with a hard, fixed, and painless mass in the anterior neck.

**Why the Correct Answer is Right**
Riedel's thyroiditis involves the replacement of the thyroid gland with fibrotic tissue, leading to a hard, woody consistency and a non-tender mass. The condition can mimic thyroid carcinoma, both clinically and radiologically, due to its similar presentation. The fibrotic nature of the mass, as observed in the open thyroid biopsy, is a hallmark of Riedel's thyroiditis.

**Why Each Wrong Option is Incorrect**
**Option A:** De Quervain's thyroiditis is a form of thyroiditis characterized by a painful, tender thyroid gland, which is not consistent with the painless, woody mass observed in this patient.

**Option C:** Hashimoto's thyroiditis is an autoimmune form of thyroiditis characterized by lymphocytic infiltration and fibrosis, but it typically presents with a goiter and hypothyroidism, which is not mentioned in this case.

**Option D:** None of the above is incorrect because one of the options (B) Riedel's thyroiditis accurately describes the condition.

**Clinical Pearl / High-Yield Fact**
Riedel's thyroiditis is a rare condition that can mimic thyroid carcinoma, and a high index of suspicion is required for its diagnosis. A biopsy is often necessary to confirm the fibrotic nature of the mass and to rule out malignancy.

**✓ Correct Answer: B. Riedel's thyroiditis**