Step 1: The key is identifying a thyroid condition where future cancer is so predictable that the gland is removed before disease appears.
Step 2: Familial medullary thyroid carcinoma occurs as part of the MEN 2 syndromes (2A and 2B), all linked to autosomal dominant RET mutations.
Step 3: Carriers almost always develop medullary carcinoma, often at a very young age, so guidelines recommend taking out the whole thyroid prophylactically once the RET mutation is documented, typically by around five years of age.
Step 4: The three thyroiditis options are benign inflammatory disorders treated with drugs, not preventive surgery, so they are excluded.
\[\boxed{\text{MEN type 2}}\]