How could being vegetarian stop animals from being eaten?

PETA said that being vegetarian would prevent animals from sufferings and being eaten by human.

We know that no matter how many people become vegetarians there would be much more meat eaters and since humans are omnivores.

Meat factories won’t close because some people refuse to eat meat, there are more and more meat eater each year in human population, and soon there would be more meat factories. They will never stop but will keep growing.

If you don’t eat the animals other people will eat them so refusing to eat animals for merely animal-loving reason won’t have any significant effect for better life for animals.

People (and vegetarian people) also have carnivorous pets and feed them with commercial pet food. How could vegetarian people think they save animals while they’re using animals meat for their own pets?

So why bother to say it will save the lives of animals when it’s actually ineffective or won’t have any effects for the actual purpose? (Remember, we’re talking about being vegetarian to stop meat-eating culture).