i am not a vegan because of animal rights, but the theories put forth by those sources are laughable. Even though under this “hypothetical situation” less animals overall would be killed, they require an “actual situation” that does not exist nor will it ever. it is true that if everyone was vegetarian, more animals would be killed than if everyone ate a meat and vegetable diet, but since there is a mixture, a person who eats meat “causes” the deaths of more animals than a vegetarian.
the theory says that crop production kills innumerable mice, voles, etc, especially when harvesting soy, which is an essential part for a vegetarian diet while animals can be raised by feeding on foraged food, therefore without the use of tractors or other methods that kill the mice, voles, etc. if you have any knowlege of the meat industry you know that pigs, chickens, and even many of the cows do not forage for their own food. the food is a mixture of harvested crops, including soy, and animals. thus in order to feed these animals, crops must be harvested using tractors, etc. also, (based on the numbers i have heard) generally for every ten servings of this food that an animal consumes, one serving of meat can be taken from it. so in addition to the crops that must be harvested for humans, in order to produce meat many more crops must be produced at a ration of ten to one.
if animals were farmed in farms like the “family farms” as Old McDonald had, then the situation would be much different. but they arent, and because of this, the theory is completely unapplicable.
you could argue though, that by trying to spread vegetarianism, you are advocating the eventual situation where more animals would be killed. 
edit: i assure you, bob, that i am eating very well. i dont know anything about nutrition, but i assumed that some types of fat are better than others, which is why i brought that up.