Hi Cmoeckel!
Happy to address why (A) is incorrect.
We can begin with the conclusion, which is that the maxim "if one ought to do something then one can do it" is not true. How does the author support this conclusion? The author uses an example, specifically a traffic jam that makers it possible to keep a promise. In other words, the author takes this to exemplify how what one ought to do (e.g., keep a promise) can sometimes be something that one can
not feasibly do (because of a traffic jam).
Next, we're given an assumption question. In reading the author's example, it didn't strike me as necessarily proving the point that the ethicist claims. For example, the broader duty might be described as a duty to keep promises that are not physically or otherwise impossible. In that case, then an unforeseen traffic jam doesn't necessarily show the maxim is not true. In that case the traffic jam might instead be described as supporting the maxim that "what one ought to do is sometimes discharged by factual impossibility." This is just putting pressure on some ambiguities in the stimulus, and then using these to pre-phrase any assumptions or flaws that the author might be making, which can equip one to tackle answer choices more quickly.
The correct answer choice, (D), ultimately gets at something like this paraphrasing. We can test it using the Assumption Negation technique. This starts with negating it:
(D) The obligation created by a promise is [...] relieved by the fact that the promise cannot be kept.
Then, we insert this negated statement back into the stimulus, and if the argument falls apart, then we know that it is an assumption on which the argument depends. If this were true, it would make the argument fall apart. The conclusion is that a given maxim is not always true, but if the obligation to fulfill a promise is relieved when it can't be kept (factual impossibility in my pre-phrasing), then the author's example doesn't in the end show that the maxim isn't true. It doesn't establish what the ethicist claims, or in other words, the argument falls apart, confirming that (D) is an assumption on which the argument depends.
Finally, take (A):
If a person failed to do something she or he ought to have done, then that person failed to do something that she or he promised to do.
It's not clear how this relates to whether the car jam example is good support or not for the ethicist's conclusion. In giving substance to the first part referring to someone who "failed to do something she or he ought to have done," presumably this is referring to failing to keep the promise. But the second part of this sentence makes the sentence instead convey that anytime someone fails to do something that the person ought to do, this failure always takes the form of breaking a promise. That seems implausible (someone who fails to avoid driving drunk ought not do so, for example, but this sense of ought isn't reducible to breaking promise). More to the point, such a claim isn't an assumption required by the ethicist.