If everyone went vegetarian there would be food shortages as an awful lot of land can only produce chicken eggs goats sheep.
If that land was to stop producing then you'd have a huge knock on effect of economics in small towns and villages that would be surrounded by scrub and no farming income.
If everyone went vegan there would be more food shortages and possibly famines as almost a third of mans food/protein comes from the sea.
Taking out a third of mankind's food supply wouldn't be a good move.