CoopedUp: If I were you, I'd find a SPDT switch with NO and NC markings (any common microswitch, or say a wall-mounted light switch), and show it to the teacher:

These markings only make sense on an electrical switch when NO and NC represent the state when the switch is not actuated. Whether there is current flowing/power applied or not, has nothing to do with the switch (unless the power is enough to break the switch); the switch controls the electrical connection. Thus, D is the correct answer.
Someone mentioned relays; they too have NO and NC markings:

However, for a relay, "actuated" state == "energized" state == "when power is applied"
to the relay coil; and "normal" state is when there is no power applied to the relay coil.
Whether there is current flowing over the NO/NC pins or not, is irrelevant. So, D is definitely still correct; C (power is not applied) is only correct if we amend the
"when power is not applied" with
"to the relay coil". Otherwise there is ambiguity in
where power is applied with respect to the relay.
In every single case, whether power is conducted through the connection controlled by the switch or relay, is completely irrelevant.
My instincts say that your teacher is in error, because they are fixated on looking at things from the point of view of controlling the current/power, instead of
controlling the electrical connection. If I were you, I'd start my objection with something like
"that might make sense if you looked at from the point of view of controlling the current/power, but in reality, a switch controls the electrical connection, and not the current or power conducted through the connection", followed by the images and text above.
We need to learn how correct
the utterance or writing, instead of the
person making it, because you are at a common task, not adversaries.
This sounds silly social games, but it is important nevertheless. It means you acknowledge that perhaps the person isn't wrong, and is simply expressing themselves poorly. It means that you do not question their knowledge, simply the way they express it. Mis-expressing stuff is, in my experience, much more common than being straight-out wrong, at least when talking with professionals.
That approach to error-correcting is fortunately very contagious, and rapidly spreads: we
feel better when our output is criticized and made better, without criticising us ourselves as a person. It also helps the lecturer, as correcting errors have much less impact on ones self-esteem, as it is questioning the
way things are put, rather than
the knowledge it stems from. I've been on both sides (student and lecturer), and it definitely works well for me.
This is also why I use a pseudonym on the intertubes: it reminds me that any and all criticism is based on my work product, and has nothing to do with me as a person, as none who use that pseudonym know me socially. (As a self-broken husk of a man, I need that sort of a social crutch.)