The carnist here claims that eating animals is justified because otherwise, they will overpopulate the earth
There is a similar claim that most carnists make that farmed animals will go extinct if we don't eat them. Both can't be true.
In addition, people love claiming that they don't eat any factory-farmed meat and only eat free-range beef. But then which one is it? Because if you have truly free and open pasture-raised everything, then there's no building to overrun anything. They would just keep grazing as normal, and you wouldn't even be able to tell that the pens have been opened.
We generally don't eat cats and dogs. Do they overrun the earth? What about other herbivorous animals like guinea pigs, hamsters, and buffalo? So there's no precedent to believe this is the case.
Keeping animals is very expensive and labor-intensive. It requires a lot of water and other resources. Farming animals in a lot of cases already takes subsidies just to keep profitable. Similarly, animal agriculture requires a significant amount of intervention, such as artificial insemination to keep the animal population at a significant enough level that we can eat and farm them. There's no reason to think they will overrun everything without the money of the animal agriculture industry pumping them up.