It's a combination of the fact that "exorcisms" are part placebo and part torture.
You see, you torture someone, they're going to make noises of pain and thrashing, signs commonly attributed to demon possession (funny how that works, huh?)
Eventually, a person exhausts themselves and stops shouting and stuff, and the exorcism stops. OR, the person keeps going until they exhaust themselves to the point of death, and suddenly, the exorcist has committed manslaughter.
If you mean the lay-on-hands method of exorcism... well, that's simple. The power of suggestion combined with peer pressure.