This is a great point, and was advanced by Steven Davis, who claimed that eating grass-fed cows would cause fewer deaths than being vegetarian. Matheny however found an error in his calculation - you can see the paper for full details, but the short version is that veg diets cause much less harm.

Yes, food has to be grown to feed cows, quite a lot of food. Apparently it takes about 10 times as much land to make a certain number of calories in the form of animals compared to other foods. So if you're worried about the wild animals being killed when you eat then that's an argument for not eating animals and animal products.

In addition to what others have said, I think it's important to distinguish between killing and suffering. The real problem here isn't the killing of animals; it's the suffering they undergo before they're killed. I don't know what it's like for those animals that die as a result of agriculture, but suppose they generally have painful deaths that last for several hours. On the other hand, animals on factory farms suffer greatly for a much longer period of time.

I suspect that most of the marginal animal suffering arising from my eating steak comes from the production of the food used to feed the cow.

I don't know for sure, but that would be pretty surprising. I know that tractors often kill animals, but I don't think it's in sufficiently high quantity to dominate.

Regardless, as you mention, eating meat requires even more grain than eating grain directly, so the vegetarian/vegan diet still results in less animal deaths.

There is one thing people seem to miss when they mention this. Some kinds of farming are more harmful than others. Can someone please tell me what foods are relatively safe?