This paper outlines the "proof" that eating pasture-raised cows kills only "7.5 animals of the field per ha would die to produce pasture forages, as compared to the intensive cropping system (15/ha) used to produce a vegan diet."
Another article written by Mike Archer also showed that more animals die in producing plant- rather than animal-based proteins.
Another paper published that same year already refuted the claim:
Davis mistakenly assumes the two systems – crops only and crops with ruminant-pasture – using the same total amount of land, would feed identical numbers of people (i.e., the US population). In fact, crop and ruminant systems produce different amounts of food per hectare – the two systems would feed different numbers of people. To properly compare the harm caused by the two systems, we ought to calculate how many animals are killed in feeding equal populations – or the number of animals killed per consumer Davis suggests the number of wild animals killed per hectare in crop production (15) is twice that killed in ruminant-pasture (7.5). If this is true, then as long as crop production uses less than half as many hectares as ruminant-pasture to deliver the same amount of food, a vegetarian will kill fewer animals than an omnivore. In fact, crop production uses less than half as many hectares as grass-fed dairy and one-tenth as many hectares as grass-fed beef to deliver the same amount of protein. In one year, 1,000 kilograms of protein can be produced on as few as 1.0 hectares planted with soy and corn, 2.6 hectares used as pasture for grass-fed dairy cows, or 10 hectares used as pasture for grass-fed beef cattle (Vandehaar, 1998; UNFAO, 1996).
So in fact a vegan diet kills fewer animals than a ruminant-only diet. This is, in fact, an argument for veganism.
The article written by Mike Archer literally has the corrections listed on the page, including that a follow-up article refuted its claims, and (if you scroll to the bottom) that it overestimated vegan crop deaths by nearly two orders of magnitude. Almost all the claims he makes are already refuted elsewhere on this site.
Even if it were true, unless one removes all non-pasture-raised animal products from their diet, this isn't the justification for one's carnism. It is a plan that avoids going 100% vegan by going more than 92% vegan. I have, to date, met no one that eats only pasture-raised beef for meat and completely abstains on ethical grounds from any other meat. So this argument (poorly) defends a stance taken by almost exactly zero people.