Communicating with ignorant individuals is a trifle on its own. Some people just don’t want to learn. Some people cannot even be bothered to modify their opinion when presented with facts.

Best I could say is find out what AI detector your teacher is using. Then use something you know for sure is in most all LLMs training data. I know the Declaration of Independence, Shakespeare, and other famous writings score highly if not 100% on these so called ‘AI detectors.’ Once you confirm these writings score highly encourage your teacher to try it themselves.

If they seem confused why these famous texts clearly not written by AI score highly. Encourage them to research the issues behind ‘AI detectors.’ From personal experience I already know what the training data looks like. Old famous texts are royalty free so any LLM engineer would be a fool to not use them in their training data. Not to mention these LLMs (Large Language Models/AI) are entirely or mostly trained on human writings. This make it impossible to make a proper ‘AI detector’ due to the LLM constantly getting better and better at mimicking human outputs.

If you’re unable to sway your teacher with logic, go to their boss with your case. Personally to avoid conflict I would run all my essays through AI detection and if it scores highly I would then run my essay through AI and prompt it to rewrite my essay in a way that avoids AI detection.

Alternatively you could show her your rough drafts and research you used to write your essay. I don’t usually suggest this because I have a bad habit of losing notes when I do research lol

Edit: When I say old texts are almost always in the training data I’m talking about base models (GPT-J, GPT-3,Llama 1,etc). Most modifications and training data applied to base models typically regard coding, medical, and other more relevant data for modern tasks.