Step 1: This is an all-except question, so we identify the one condition that does not warrant a new liver.
Step 2: Biliary atresia destroys the bile ducts in infancy and is the leading paediatric reason for transplantation. Primary sclerosing cholangitis progressively scars the biliary tree and end-stage cirrhosis from any aetiology destroys hepatic function; all three are standard indications.
Step 3: Hepatitis A, by contrast, is an acute fecal-oral viral illness that almost always clears completely and leaves no chronic injury. With no irreversible damage there is nothing to transplant for.
Step 4: Hence hepatitis A stands out as the exception.
\[\boxed{\text{Hepatitis A}}\]