The defeat of the Inca by the Spanish can be attributed primarily to the refusal of the Incan emperor to cooperate with the Spanish. This refusal played a significant role as it led to conflict and resistance against the Spanish invaders. Additionally, the Inca were unprepared for the Spanish conquest, which was facilitated by factors such as the Spanish's superior weaponry, the spread of diseases that weakened the indigenous population, and internal divisions within the Inca Empire.
While the other options mentioned have elements of truth, the cooperation and response of the Incan leadership under Atahualpa was a decisive factor in their defeat.