In the story from gulliver's travels of how the dispute arose between the big-endians and the little-endians, the chief objects of swift's satire are

Triviality and pettiness.  

Explanation:

In Jonathan Swift's "Gulliver's Travels", the protagonist Lemuel Gulliver is the source of Swift's satirical and even outbursts for criticizing the political situation of England. He also uses the numerous characters to satirize the English government and the society as a whole.

In Chapter 4, Reldresal had narrated to Gulliver how the two nations of Lilliput and Blefuscu first came against each other. The issue being the mere order of the then king to break their eggs from the small end, leading to the division among the people into Big-endians and Little-endians. This led to massive uproar, where "one emperor lost his life, and another his crown". Moreover, "eleven thousand persons have at several times suffered death, rather than submit to break their eggs at the smaller end". This trivial issue which led to such massive conflict is a satire upon the trivial and petty nature of English people to easily get into conflicts.

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