In past 17 years as a professional molecular biologist, this is for the first time I have read such a ridiculous statement on conservation biology and that too with reference to supposedly "
deeper science". Species (animal or plants) go extinct ONLY when they are harvested from the wild and in an uncontrollable fashion. Cattle on the other hand are domesticated animals and, as @
Chak Bamu has correctly pointed out, will continue to thrive (let alone survive) being important economic commodity.
Even if the cattle go extinct, other species wont go extinct because cattle (or other domesticated animals) are not the only species which contribute to the soil fertility. Any living thing that consumes nutrients and discards the waste as excreta contributes to soil fertility, from a humble earthworm to the human.