Tell that to those who lived under the Soviet collective laws. They were allowed something like 1/2 acre to grow food for their families. Those little patches produced a significant amount of the food that wasn't grown on the collective farms.
Of course, a lot of that had to do with incentives....
Oh you can totally feed your family with a half acre. If you're good at it you can feed several families.
If you only grow and eat potatoes, you can feed 7 people 2000 Calorie/day diets all year. That's the figure if you grow potatoes like big potato farmers. If you nurture the land and integrate other species taking advantage of differing growing seasons and do all you can to make perfect soil conditions, you can get a lot more out of it than potatoes every day for 7.
Of course, a lot of that had to do with incentives....