The general thought is:
A .22 caliber bullet doesn't have enough impact force to stop a human being, *especially* if they're on an adrenaline high. There are documented cases of people being shot with 22s or 9mm handguns 20 or 30 times and *still* reaching the person with the gun and hurting them.
Most police departments now are moving to 44 or 45s because they *stop* people who are running toward them because the impact force tends to knock people over or spin them around.
Statistically, *most* gunshots happen within something like 30 feet, and that gives a person with, say, a knife, *more* than enough time to run at you before you get enough 22 shots into them to stop them. An interesting read on this is the book "On Killing" by a Lt.