The student is right, if she has no idea what "a term" means, how can she learn what to do. Like sit deep in the saddle, or inside rein, outside leg, just to name a few.
This is an excellent article. I agree that flexibility from the teacher is key. Especially when some students can have a bit of the engineer and artist all at the same time. Kudos to you for not giving up and succeeding in both learning and teaching. You seem to have a true, compassionate teacher's heart.