I've seen a bunch of "I need to get off this plane RIGHT NOW!" scenarios over the the many years I've flown commercial. They ranged from genuine medical emergencies to self-induced medical issues, from panic attacks to full-blown psychotic episodes.

In every single instance, I'd rather the person get off the plane before we leave the gate, or before we leave the ground, no matter how much of an inconvenience it might seem to be at the time. Dealing with a sick/frightened/loony person at altitude is much less fun than getting delayed or stuck somewhere, and being diverted is often much worse than never taking off.