The article's author leads with his main point: self-confidence is a dangerous virtue. He supports this point by arguing that self-confidence "often degenerates" into arrogance, and that the danger of arrogance should be obvious. He appeals to history by pointing out how "much more humane" the twentieth century would have been without the arrogance of Hitler or Stalin.
This is a bit of an unusual stimulus. It uses a number of argumentative strategies that don't show up too often on the LSAT: emotionally charged language, an appeal to "common sense" ("evident to all who care to look"), etc. Especially for this EXCEPT question, it makes the most sense to go right to the answer choices and proceed by process of elimination.
The author attempts to persuade ββ βββββ βββ ββ βββ βββββββββ ββββββ
using extreme cases ββ βββββ ββ βββββββββ ββββββββ
This accurately describes something the author does: he appeals to Hitler and Stalin as extreme cases of arrogant self-confidence. So (A) isn't the answer choice we're looking for.
introducing value-laden terms, ββββ ββ ββββββββββ
(B) accurately describes the method of reasoning. The author uses plenty of value-laden language: not just "vice," but "degenerates," "care to look," etc. So (B) isn't the answer choice we want.
illustrating the danger ββ βββββββββ
The author does illustrate the danger of arrogance, specifically mentioning the effect the "arrogant self-confidence" of Hitler and Stalin had on the twentieth century. (C) describes something the author does, and isn't the answer choice we want.
appealing to authority ββ ββββββββββββ ββ βββββββββ
While the author does use the phrase "evident to all who care to look," this isn't so much an appeal to a specific authority as a rhetorical set-up for the specific illustration he uses next. Since the author doesn't use an appeal to authority to substantiate his claim that arrogance is dangerous or that self-confidence is a dangerous virtue, (D) is the answer choice we want.
implying that Hitlerβs βββββββββ βββββ ββββ βββββββββββββββ
By claiming that self-confidence is dangerous because it often degenerates into arrogance, and then alluding to Hitler as an example of "arrogant self-confidence," the author does imply that Hitler's arrogance arose from self-confidence. So (E) accurately describes the method of reasoning, and isn't the answer choice we're looking for.