That doesn't make any sense. Animal products take up way more space than vegtables, both directly and indirectly (most of the plants we grow are to feed the animals). If everyone were to go vegan, we would actually save huge amounts of space (and also effort, water...), so it's very achievable.
This can be true for intensive farms using cereals and legumes as fodder, but if we just ate LESS meat, but higher quality one, from mostly grazing livestock, in that case animals can transform into high quality food plants that are inedible or either not tasty or not nutritious or both for humans, like grass, acorns, very bitter bulbs and tubers, etc. or even plants that are poisonous for humans and some animals, but edible for others. Game can also give food from woods without modifying them, so hunting, following well thought rules, animals like wild boars, that in many countries have only humans left as predators and so aren't currently threatened but even in excess can even be good for the environment. Reintroducing wolves wouldn't work for wild boar population control, as wolves aren't stupid and they'd kill any other animal available before hunting an animal difficult and dangerous. Almost the same applies in a few places where even deers have become too many due to lack of other predators than men. The key is minimising environmental impact, agriculture alone isn't the right solution, intensive farming neither, maximum diversification and the right choice of food to take from each place are. Obviouly for the new human ecosystem to not just work, but also be sustainable in the long term, the weekly amount of meat eaten should be much lower than the average current one in the USA. Greater diversification than now will also be necessary very soon in fishing. (*)
(*) PS: And in agriculture too.