Final answer:
The incorrect reason for Cortés's conquest of Tenochtitlan is the claim that Montezuma wanted the Aztec Empire to join New Spain. Hence the correct option is (2).
Step-by-step explanation:
The answer to the question, which was not a reason Cortés was able to conquer Tenochtitlan, is option 2: Montezuma wanted the Aztec Empire to be part of New Spain. This statement is incorrect as there is no historical evidence suggesting that Montezuma II wanted the Aztec Empire to become part of New Spain.
Instead, various factors played a crucial role in Cortés's victory, including smallpox that devastated the population, military alliances with indigenous tribes like the Totonacs and the Tlaxcalans who opposed Aztec rule, and the superior weaponry of the Spanish such as steel swords and firearms. These elements, combined with strategic tactics like taking Montezuma hostage, created a clear advantage for the Spanish over the Aztec forces in Tenochtitlan.