What is the ruling on a female student treating men during training, and the trainer holding the female student's hand to train her in tooth extraction?

It is permissible for a woman to study dentistry if it suits her nature, provided it adheres to Islamic guidelines. If you can avoid treating men and training under a man who touches your hand, or if you can transfer to a university that observes Islamic guidelines, then do so. If that is not possible, try to avoid training under this man or persuade him to use another teaching method that does not involve touching your hand. If that is not feasible and there is a necessity for this study, then your treatment of men should be limited to what is necessary, while avoiding looking at or touching the awrah al-mughallazah (severe nakedness), and wearing gloves to avoid touching a man's hand. You must fear Allah and adhere to proper conduct and modesty.