He was reportedly sitting in a window seat, while the owner of the emotional support dog was sitting in the middle seat.
Maddox-Peoples said the dog appeared to be a lab mix weighing approximately 22kg.
Another passenger told Fox 5 that Delta crew members were heard saying the dog's owner was a "combat veteran" and that after the incident, he was seen cradling the dog in the gate area and crying.
Allegedly, the cabin crew said the man was heard repeatedly saying, "I know they're going to put him down".
In a statement to Fox 5, Delta confirmed the incident.
"Prior to pushback of flight 1430, ATL-SAN, a passenger sustained a bite from another passenger's emotional support dog. The customer who was bitten was removed from the flight to receive medical attention. Local law enforcement cleared the dog, and the dog and its owner were re-accommodated on a later flight; the dog will fly in a kennel."
The United States allows passengers to take animals on board a flight at no extra cost, but only if they cannot function without the animal's support.
In recent years, a variety of unusual emotional support animals have made headlines around the world.
An emotional support duck - named Daniel Turducken Stinkerbutt - was photographed on a US flight and quickly went viral on Twitter.
An emotional support pig was also spotted on a flight to the Virgin Islands.
However, the vague rules around these travelling companions have sparked fierce debate, as reported incidents of disruptive pets rise.
USA Today reported that airlines were pushing the government to adopt a more restrictive definition.
In New Zealand, we're unlikely to see pigs fly anytime soon.
While Air New Zealand allows some service dogs on board, this does not include emotional support, therapy, comfort or psychiatric service dogs.