Example 2 does not necessarily call for us to use a contrapositive. The author seems to be making an attempt at a contrapositive, but does not do so correctly. We don't need to correct this mistake, but rather we need to find an argument among the answer choices that makes the same mistake.
As seen in the video, the premise states that a doctor who fails to answer a patient's questions (FAQ) cannot be competent (not C).
FAQ - - - - - - - - > not C
The author attempts to reverse these conditions, but makes a reasoning error by confusing sufficient and necessary conditions.
We cannot assume that:
not FAQ - - - - - - - > C
You mentioned answer choice E.
Premise: HT and SW - - - - - - - - -> not STB Premise: Jeremy is strong-willed. Conclusion: Jeremy will not succeed in this business.
The author's reasoning can be diagrammed like this: SW - - - - - - - - - - -> not STB
The author completely leaves out one of the sufficient conditions. This would be correct if "or" was used rather than "and," but that was not the case. We did not need to create a contrapositive in order to detect this error. It is an error, but not the same one used in the passage, which is why E is incorrect.