Not necessary, because the argument concerns what the student SHOULD do if he made a certain promise to Jeanne. What other people actually do concerning truth-telling doesn’t affect what the student should do.

Not necessary, because we don’t know what is in Jeanne’s “best interests.” Nothing in the argument commits the author to some view about what would be the better course of action for Jeanne’s interests.

Not necessary, because the consequences of a broken promise are irrelevant to the reasoning. Although the author does believe that the student should not break the promise he implicitly makes, we have no reason to think that this has anything to do with the consequences of broken promises.

Necessary, because if it weren’t true — if NO implicit promises are worse to break than ANY explicit ones (or in other words, if every explicit promise is worse to break than every implicit promise) — then we have no reason to think the student should honor his promise to the teacher over the promise to Jeanne. The promise to the teacher is implicit; but the promise to Jeanne is explicit. The negation of (D) would imply the student should lie to the teacher in order to fulfill the promise to Jeanne.

Not necessary, because the author’s argument encourages the student to break the promise to Jeanne. So clearly the author does not have to believe that one should never break a promise.