if he's wrong, please explain why he's wrong
There's no question on the point that if an animal population is stable and it's rate of reproduction is faster than the rate of death from natural causes (this is true of all animals unless they practice birth control) then the average age at death will be less than the average age of death from old age. The greater it's reproductive rate the greater the difference.
The graphic posted gave the "natural life span" of various animals but really meant the average age of death from old age. The life span of an animal in nature is necessarily much shorter. A few animals do manage to get this old in nature but they are like lottery winners. Most of the losers don't make it out of infancy and they drag the average down.
What's more interesting is how someone could be blind to such an error. It requires you to be in ignorance, willful or otherwise of the most fundamental characteristic of life, the engine of evolution. More animals are born than survive to reproduce, this is how natural selection adapts animals to their environment.
All animals get sustenance by harvesting the excess reproduction of plants or other animals. By animal husbandry and agriculture humans essentially insert themselves in the place of the carnivore or herbivore or disease or circumstance which would in the course of nature have harvested or limited the excess reproduction.