The words "trifle" and "triviality" are likely the most tempting wrong answers, as they both indicate unimportant things. Clearly the first blank pertains to something that is not very important. Note, however, that it is about something that is unrepeated. An anecdote is a little story about something unique and without parallel. At best, it is a lone fact but not necessarily a justification for a complete theory of something that is important. (Hence, we have the expression "anecdotal evidence," informally meaning, really just based on some stories from some particular people.) The matter at hand, however, was actually very important, or so it seems. Hence, it was a matter of "significance" (a word that is clearly related to "significant").

The word "antinomianism" primarily pertains to a certain doctrine held by some Christians regarding the need to follow moral laws. The word itself can be used in a general sense (though rarely) to describe someone who is "anti-law." If nothing else, this sentence is an exercise in word roots. The "anti-" prefix means against. The remainder of the word is related to words like "autonomy" and "anomaly." An anomaly is not merely something that is strange, it is actually something that goes against the expected laws (e.g. the laws of nature, custom, etc). Likewise, "autonomy" is not just about being free, it actually means able to give oneself a law to follow. Hence, these words build on the Greek root "nomos," meaning law. This is what is being described in the youth.

As for the second blank, it seems that they show contempt in the face of the law. Hence, the word "defiance" is a good option for the second blank.

Notice the sentence shift, indicated by the word “but.” This indicates that the word in the first blank must be the opposite of "virtues." “Affection . . . evasion” and “passion . . . obsession” can be eliminated. Since a liking for cigarettes is commonly looked down upon, we can reasonably assume that “vice . . . affinity” is the correct answer.

“Peccadillo” and “misdemeanor” are used for minor offenses, so it would be a stretch to say that they warranted a “manhunt.” A “scandal” is a disgraceful event, and an “accomplice” is someone who helps in a wrongdoing. These two form the right response.

“Cynophobia” is a fear of dogs. “Agoraphobia” is a fear of places where it might be difficult to escape. “Mysophobia” is a fear of dirt or filth. And the common “arachnophobia” is a fear of spiders. “Vertigo” is a reeling sensation, as if one is about to fall. “Acrophobia” is a fear of heights. These last two form the correct answer.

“Austerity” somewhat works; though, it should be noted that “austere” describes self-denial and simple without pleasure. Also, know that “dearth” and “paucity” refer to scarcity. “Frugality” is the quality of not being wasteful. "Nimiety" refers to having an overabundance. Together, these form the correct answer.

“Aegis” comes from a very similar Greek word, which was the name of the shield of Zeus. It is often used in the phrase “under the aegis of,” and it basically means a protection or support, as you would expect from being named after a god’s shield. A “coalition” is a group of people who join together for a common cause. “Aegis . . . coalition” is the correct answer.

"Perspicacity"  makes sense in this context, as his intelligence would be one reason he chooses not to acknowledge his mistakes. This answer is also close to another, "shrewdness", so the second word becomes crucial to picking the proper answer. "Obfuscating" is the only word that makes sense here, as it matches the description of the confusing talk in the same clause. This also illuminates "perspicacity" as the correct answer, as the verb "leaping" tied to "shrewdness" doesn't make sense.

"Ebullience" means enthusiasm and positivity. An "elegy" is a mournful poem or song about a dead person. "Cynicism" and "tirade" are the closest wrong answers, but a "tirade" doesn't demand a mournful tone.

"Grandiloquence" is pompousness in speech. "Tenacity" is persistence in a task in the face of adversity. "Quiescence" and "acumen" are grammatically correct in this sentence, but "grandiloquence" fits better because it suggests speaking, while "quiescence" suggests silence.