A predator population can only increase until the prey population drops as a result of too many predators. Then the predators die off, and the prey population rebounds. At that time, the predators once again have sufficient food, and their population grows. Then the prey population starts to decrease. Etc.
The boom/bust cycles of predator and prey population numbers have been going on for as long as there have been predators and prey.
How dare you enter the fray with the logic of thousands of years on your side. If you continue to do this you will prove the nut jobs wrong and political correctness will not allow that to happen.
Now go to your room.
That theory is very outdated. Isle Royale has 1200 healthy moose and only 3 wolves left. Your theory sounds very close to natural balance - a theory that has been completely debunked. It has been replaced by chaos theory and in fact is way overly simplistic. Herds of caribou have been depleted beyond recovery in BC by newly introduced wolves. The wolves are thriving.