Reason from the direction each factor pushes blood glucose. Fasting hypoglycemia means the body fails to keep glucose up while not eating, so the culprits are conditions that cripple the liver's ability to release or make glucose. Glucose-6-phosphatase deficiency blocks the final dephosphorylation step shared by glycogenolysis and gluconeogenesis, trapping glucose inside the liver and dropping blood sugar (von Gierke disease). A cirrhotic liver has lost both its glycogen reserve and its gluconeogenic capacity, so fasting tips the patient into hypoglycemia. Glycogen synthase deficiency means barely any glycogen is laid down, so once meal-derived glucose is gone there is no store to draw on and glucose falls. Glucagon, in contrast, is the hormone whose entire job is to push glucose upward by driving glycogen breakdown and gluconeogenesis; too much of it produces high glucose, the opposite of hypoglycemia. So the odd one out is glucagon excess.
\[\boxed{\text{Glucagon excess}}\]