where are the statistics for that? Would we truly cause other species to go extinct? or is that that just your opinion? where are the facts?
the fact is, there are many carnivores and omnivores besides humans, have any of them caused an extinction?
in addition, most carnivorous animals don't eat the entire animal, they eat what they can and leave the rest for the insects. humans on the other hand store their the meat and can feed off the meat from an animal for a long time.
a single 75 pound deer can feed one human for about a month(this I know for a fact, I live with hunters)
but deer are not the only animal to eat, a single rabbit can last a week as well as a pheasant.
a moose for a single person could give you enough food for 1 year
now lets look at something else a moose can give birth in 8 months and they can give birth to 2 baby mooses.
my point being, we would not cause another species to go extinct by eating them, on the contrary avoiding eating other animals would cause their populations to become stagnant(take differential equations/calc based zoology)
I agree farming large populations of animals can be bad for the environment, but I think that if hunting was more common extinctions would occur less, because a lot of extinctions actually happen because of land cleared for farming, not from hunting.
the only case of hunting causing an extinction would the Dodo bird, but that was only because we invaded the ecosystem there. humans are just as much a part of the ecosystem in America and Europe as wolves, bears and foxes, so hunting would not cause problems.
actually the most commonly hunted animal in America are fish.
we call it fishing, but technically its a form of hunting, using a trap.