We need animals for sustainable farming
Manure is one route to soil fertility, not the only one. Stock-free systems using green manures, composts and rotation are established, if less common.
A farm that works with nature rather than against it relies on animals as part of the cycle: grazing stock turn grass and crop residues that people cannot eat into food, their manure returns nutrients to the soil, and they make productive use of hill and pasture land that could never be ploughed. Take the animals out and that closed loop breaks, leaving growers dependent on bought-in synthetic fertiliser and squeezing more out of arable land that already struggles. Animals are not an optional extra in sustainable agriculture but one of the things that makes it sustainable in the first place.
Mixed farming does have genuine agronomic logic: animals convert material humans cannot eat, return nutrients to soil, and fit land unsuitable for cropping. Integrated systems can work well, and dismissing that is a mistake.
It does not establish necessity. Stock-free organic systems maintain fertility with legume rotations that fix atmospheric nitrogen, green manures, composted plant material and careful rotation, and have been certified and operating commercially for decades. They are a minority of production, which reflects economics and convention more than agronomic impossibility. The relevant comparison is also at system scale: a food system routing most of its calories through animals needs far more land in total than one that does not.
Presenting two options as though they were the only ones available when further options exist. Also called a false dichotomy, or black-and-white thinking.
How it applies here: Treats livestock as the only available source of soil fertility, when legume rotations, composts and green manures are in established commercial use.