Spanish conquistadors were outnumbered by the incas, yet the incas were defeated when their leader, atahualpa, was tricked into being captured and was then killed. the spanish believed they were justified in going to war with the incas because
the spanish had made a treaty with atahualpa's enemies.
the spanish were out of food and the incas wouldn't feed them.
atahualpa refused to convert to christianity.
atahualpa was going to return to his capital to build an army.