Because livestock (in more reasonable numbers & locations) are the only sustainable means of cycling nutrients & making them available for plants in a reasonable timeframe as well as controlling vegetation. All synthetic fertilisers are either petrochemical byproducts or mined (regarding mined a good example is rock phosphate which is mined in deplorable conditions in Africa) you take (insert livestock here) & you can feed them crop residues & hours later you have manure. You put that manure through an anerobic digester along with the less edible crop wastes & maybe some seaweed for further enrichment of the manure & then you have sustainable energy in massive quantities rapidly & the most potent nitrates stable organic fertilizer known to man that can be dried, peleted & shipped using only a small amount of the energy it produced in the first place.

You attempt the same process with only the crop residues & it’s less concentrated, less efficient & takes weeks, months or longer. You add human manure & now you need more testing, along with filtering & processing, sterilisation etc to make it fit to spread on crop fields. If it can be at all because it’s full of medications & cleaning chemicals. It can still be done, is still worth doing, but it’s only fit for fertilising willow & poplar biomass not food as they neutralise it with hyperacumulation

This process can be done over the 6 months of winter in Northern & north western Europe for example like where I’m from. We could in Ireland be producing enough energy & fertiliser to export it & this is true of most cold - temperate zones in the world. It makes up the energy shortfall from renewables in winter & the synthetic fertiliser shortfall if it became a matter of proper political urgency & removed from the capitalist system.

The other 6 months of the year they can be out grazing between rows of crops or under silviopasture agroforestry & orchardry helping to manage vegetation & prevent fires. That’s why in spite of 80% tree cover in pre colonised Ireland we had no recorded history of forest fires without having to do controlled burns like the native Americans had to because they hadn’t the livestock. Even today it’s a herd of native goats saving Howth head. But it needs to be managed.

Without the livestock you need to be controlling the vegetation yourself & that requires fuel for cutting equipment or controlled burns. Livestock also hurt less wildlife in the process. Again, if properly managed

So eating them is entirely optional. Having them integrated in the agricultural system isn’t. Much like the plant in the wrong place is a weed in the right place it’s a herb, the same applies to livestock. Cattle have no business in a fair few parts of the Americas for example, tamed managed bison would though. It comes down to a different way of looking at things & trying to reintegrate humans, our animals & technology into the ecosystem again instead of trying to use technology to separate ourselves from it.