The objection
"If everyone went vegan, the world would be overrun with cows, pigs, and chickens, because nobody would kill them anymore."
Problem 1: even then, there'd be less suffering
Even if that happened, such a world would probably have less suffering than today's, where tens of trillions of animals are killed every year. And in a vegan world, people would care about animals and look for ways to take care of them.
Problem 2: the opposite would happen
This is the main problem. Today there are billions of cows, pigs, and chickens because humans make them be born, through controlled breeding on farms. These animals aren't "left over" in nature: they're produced.
If people stopped buying animal products, farmers would stop breeding the animals. The number of farmed animals would drop, little by little, as more people went vegan.
It wouldn't happen all at once
The world doesn't go vegan overnight. The change would be gradual. Each year, fewer animals would be born for exploitation.
In short
- Even a world with more animals would have less suffering than today's.
- Farmed animals exist because humans make them be born.
- In a vegan world, there would be fewer farmed animals, not more.