This argument assumes that livestock eat plants that could have been eaten by humans, and that's not the case in most instances. It also assumes that all land currently grazed by livestock is suitable for farming, which is obviously not the case without a great deal of expense.
And I'm not denying the antecedent, you're proposing a false dilemma. Just because current methods of factory farming are inefficient doesn't mean we need to stop eating meat to fix the problem.
In that case, they aren't valid since improving the process to be more humane and efficient is hugely preferable. It doesn't involve giving up several species which have become domesticated and wouldn't survive in the wild, and are our only naturally occurring sources of vitamin B12. You'd also have to prove that there is enough arable land to provide enough of a plant-only diet for the entire world.
Extreme measures like completely giving up meat on a voluntary basis are completely untenable. The amount of resources we'd have to expend selling such an idea would be cost-prohibitive, and quite frankly, I think would work about as well as any other kind of prohibition has worked with humans, especially omnivorous humans.
Methane from livestock doesn't contribute to the net gain in greenhouse gases because the CO2 obtained from methanogenesis is from sources that used up atmospheric CO2 in the first place. I can search for a paper which shows this, but what you're suggesting is killing off the world's livestock in order to prevent them from burping. How is this a viable solution?