**Core Concept**
Liver transplantation is a complex surgical procedure that involves replacing a patient's diseased liver with a healthy one. To determine the correct answer, we must consider the underlying conditions that make liver transplantation contraindicated.

**Why the Correct Answer is Right**
Liver transplantation is contraindicated in patients with certain types of cancers, particularly hepatocellular carcinoma (HCC), that have metastasized or are unresectable. This is because the transplanted liver may harbor residual cancer cells, leading to recurrence and poor prognosis. The Milan Criteria, which include a single tumor ≤5 cm or up to 3 tumors ≤3 cm, are often used to select patients with HCC who are suitable for transplantation.

**Why Each Wrong Option is Incorrect**
**Option A:** Primary sclerosing cholangitis (PSC) is actually a relative contraindication for liver transplantation, as it is associated with a high risk of recurrent disease and cholangiocarcinoma in the graft.
**Option B:** Cystic fibrosis is a condition that can be managed with liver transplantation, as the procedure can improve nutritional status, reduce complications, and increase life expectancy.
**Option C:** Primary biliary cirrhosis (PBC) is a condition that can be managed with liver transplantation, as the procedure can improve liver function, reduce symptoms, and increase life expectancy.

**Clinical Pearl / High-Yield Fact**
Remember the "Milan Criteria" for selecting patients with HCC for liver transplantation: a single tumor ≤5 cm or up to 3 tumors ≤3 cm.

**Correct Answer: D. Patients with metastatic or unresectable hepatocellular carcinoma.