“We’ll be overrun by farm animals” or “What would we do with all the
animals?”

    "I get the question of ‘what we are going to do with all
    of the animals when the world goes vegan?’ quite a
    bit. This question always amuses me. As if the world is
    going to all decide to go vegan at the same time. I
    would like to state for the record that I would be happy
    to be in charge of this issue when everyone decides
    to stop exploiting animals. But since people seem to
    show concern, I will answer it as seriously as I can. In
    no scenario would the world ever go vegan at once so
    there would never be billions of farmed animals
    needing care or homes. As people slowly stopped
    consuming animals, ‘farms’ would stop breeding them.
    Eventually you'd be left with some amount of animals
    and a mostly vegan world. At that point, they could go
    to existing sanctuaries or we could create additional
    sanctuaries so that they could live out their lives in
    peace. The key is to stop breeding animals, which
    only happens when people stop consuming them."
    - The Thinking Vegan