Final answer:
Moctezuma allowed Cortés into Tenochtitlan due to a combination of perceived divine connections, awe, diplomatic tradition, and political strategizing, which inadvertently led to the Aztec Empire's downfall.
Step-by-step explanation:
The Aztec chief Moctezuma allowed Hernán Cortés and the Spanish conquistadors to enter the capital of Tenochtitlan for several complex reasons. One leading hypothesis is that Moctezuma might have believed Cortés was a god or had divine connections perhaps related to the deity Quetzalcoatl, though this interpretation comes mainly from Spanish accounts and might have been exaggerated.
Moctezuma did initially treat the Spaniards with respect and hospitality, offering gifts, and according to Cortés, Moctezuma regarded the King of Spain as a natural overlord. However, historical evidence points to political stratagems and attempts to maintain power by controlling these visitors. Eventually, this misjudgment, along with the Spanish alliances with enemies of the Aztecs and the spread of disease, led to the downfall of the Aztec Empire. The initial welcoming attitude might have stemmed from a combination of awe, diplomatic courtesy, belief in omens, and perhaps a significant underestimation of the Spanish intent.