The teacher accuses the student of using the LLM to perform the task they are assigned. This entails not properly understanding the assignment and presenting an accomplishment which has not been achieved by the student themselves.
On the other hand the teacher using an LLM tool also do not understand the reasoning of the decision and present often present them as their own judgement. A judgement that has not truly been felled by the teacher because they do not use the tool for understanding but for deferring their responsibilities.
In doing so the teacher is engaging in the same act of (self-)deception they are accusing the student of: presenting an achievement not truly reached through their own understanding, even if the situation necessitates it (non-deferrable learning vs. non-deferrable decision).
The use of LLM-detection in this way thus mirrors the very problem it seeks to address.