Cottonmouths have a reputation for aggression that outstrips the evidence. In a widely cited study, researchers approached, stood beside, stepped on with a boot and picked up with an artificial hand a large sample of wild cottonmouths. Most attempted to escape; many gaped or vibrated the tail; only a minority bit, and then largely when actually restrained.
The gape itself is the display the common name records: the mouth opens wide to expose a startlingly white lining, held toward the threat. It is a signal that pairs with musk release and tail vibration, and it works because a snake that has warned does not need to spend venom.
Much of the pursuit folklore comes from misidentification. Harmless water snakes of the genus Nerodia share the habitat, are far more abundant, swim with the body submerged rather than riding high, and flee toward water, which can carry them past a person on the bank. Distinguishing the two in the field is genuinely difficult from a distance.