Step 1: Frame the surgical problem.
Before surgery, a solitary nodule is of uncertain nature. The operation must remove it safely and also let the pathologist tell whether it is benign or malignant.
Step 2: Work out the operation that meets both needs.
Taking out the entire lobe holding the nodule, plus the isthmus, gives a full specimen with clean margins and settles the diagnosis in one step. This procedure is hemithyroidectomy, also called thyroid lobectomy.
Step 3: Plan the next step if needed.
Once the pathology comes back, a benign result means no further surgery is needed. A malignant result can be followed by completing the thyroidectomy on the other side in a second planned operation.
Step 4: See why the bigger operations are premature.
Total and subtotal thyroidectomy both act on the whole gland right away, which is unnecessary when only one side has a defined lump of unknown nature, and both add avoidable risk to the parathyroids and the nerves supplying the voice box.
Step 5: See why enucleation is unsafe.
Peeling out just the nodule without a rim of normal tissue around it does not guarantee a clean margin, so it is not used in modern thyroid surgery.
\[ \boxed{\text{Hemithyroidectomy}} \]