Why The FCC dropped the mandatory logging requirement for amateur stations decades ago, so keeping a log is voluntary. Amateurs still log because a record of dates, times, frequencies, power and contacts lets you answer intelligently if the FCC or a Volunteer Monitor asks about your operation, for example after an interference complaint. Logs also support QSLing and awards, but the exam answer focuses on documenting what your station was doing and when.
Watch out The choices about the FCC requiring logs of international contacts or third-party traffic sound plausible but no such logging rule exists in Part 97; license renewal is also purely administrative and never depends on proving operation.
No FCC rule says log it, but a log is your best witness if the FCC comes asking.