What would cause a patient to bite down hard during intubation?

That would. Probably be an emergency forced intubation. An intubation for general anesthesia will involve a muscle relaxant and a nerve stimulator after a dose of Propofol that that is effective immediately.
Not yet ready. The patient is usually asleep before attempt of intubation. Sometimes however the medication has not been given time to take effect fully (every pt reacts differently). But this can be quickly addressed by the anesthesia provider.