Main Crux

US has shown that formal education is a must for the smooth functioning of democracy as peopple become aware of their rights.

The author develops the argument by

(A) using an analogy to establish a precedent for a planned future event

Yes quite close. It is indeed an analogy on previoue event and present democracy. But the giveaway is "planned future event" we are talking of democracy in general and not some planned event.

(B) illustrating differences in the requirements for the functioning of a democracy depending upon the democracy in question

Out of context. There are no differences being talked of.

(C) introducing an example that illustrates a common principle

This answer choice fits in properly. US democracy is an example and the successful running of democracies is a common principle.

(D) forming a hypothesis that explains apparently contradictory pieces of evidence

Out of context. No hypothesis is being talked of and no contradictory pieces are produced.

(E) supplying an alternate explanation for a known phenomenon

There is no alternate explanation rather the author follows the same line of reasoning.

Answer: C