The Preamble quote that most specifically refers to natural rights: "[T]hey are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.”
John Locke was one of the first of the Enlightenment era philosophers. The Enlightenment's emphasis on reason was in contrast to superstition and traditional beliefs. The Scientific Revolution had shown that there are natural laws in place in the physical world and in the universe at large. Applying similar principles to matters like government and society, using reason will guide us to the best ways to operate politically so as to create the most beneficial conditions for society. This included a conviction that all human beings have certain natural rights which are to be protected and preserved. Locke's ideal was one that promoted individual freedom and equal rights and opportunity for all. Each individual's well-being (life, health, liberty, possessions) should be served by the way government and society are arranged.
Answer:
The Spanish were trying to make the Aztec leader out to be a coward and weak.
The Spanish were attempting to give the impression of being powerful with their animals and technology.
Perhaps the Spanish were trying to give the impression that they were likely to win—thereby attracting more indigenous allies.