Final answer:
An independent Mexico would offer the benefit of a loss of European influence in the Americas to the United States. Therefore, the correct option is D.
Step-by-step explanation:
Gutiérrez believed that an independent Mexico would offer the benefit of a loss of European influence in the Americas to the United States. This is because Gutiérrez, as a Mexican revolutionary, wanted to free Mexico from European control and establish a sovereign nation.
A free and independent Mexico would weaken European power in the Americas and potentially open up opportunities for the United States to expand its influence in the region.