That's silly. We bring billions and billions of animals into existence every year. It's not a natural or inevitable process. If we stopped eating meat, we'd stop breeding them.
I think you're leaving out a lot of factors, like methane production from cattle, how cutting down forests for the purpose of grazing reduces the land's ability to absorb greenhouse gases, etc. But this isn't really something I'm super knowledgable about, as I'm vegan primarily for animal rights...