Hannibal Barca's strategy in the Second Punic War was more sophisticated than simple military genius — it was a political strategy dressed as a military one. Hannibal's goal was not to destroy Rome (he brought no siege equipment capable of threatening a walled city) but to detach Rome's Italian allies by demonstrating Roman vulnerability.
Cannae in 216 BC was the tactical masterpiece everyone knows: double envelopment, annihilation of roughly 50,000-70,000 Romans and allies in a single afternoon. It remains the most studied battle in military history. But Hannibal won at Cannae and still lost the war.
The answer is that the Italian allies mostly stayed loyal to Rome. Rome's web of obligations, colonial settlements, and carefully calibrated alliance relationships held under conditions that Hannibal had assumed would fracture them. Without a base of supply in Italy, Hannibal's army slowly eroded through attrition.
Fabius Maximus understood Hannibal's strategic logic and countered it correctly: deny him the decisive confrontation he needed. The broader lesson is that military genius operating under an incorrect political theory of the enemy doesn't win wars. Hannibal was right about Roman tactical rigidity; he was catastrophically wrong about Roman alliance loyalty.