"they die from being eaten, from disease, or starvation"
This is true in the animal kingdom as well. Especially for a farm animal, being eaten. If wolves can catch deer or elk, they can catch a cow. I mean you've seen cows right, not very fast. :) This is also an unfortunate consequence when animal rights activists decide to release domesticated animals, they don't know how to survive in the wild. My family would always take cats people didn't want anymore on our farm, and they disappeared quickly. We assumed coyotes, because their parents didn't teach them how to be careful. :( Instinct can only get you so far, you need to be taught as well, and generations in captivity means the parents didn't know what to teach.
And food gets scarce in winter. I was watching a documentary where one chipmunk was storing acorns, and another was hiding nearby, and just stealing them. I don't remember the name, but it was on netflix, and it was focused on high speed, high resolution camera work. The animals seemed to be an excuse to use the cameras, lol.
Also, if I had to die, I'd rather have a humane execution like a farm animal, rather than being eaten or starving. I know there are 'documentaries' that portray suffering on farms, but the farmers I know take good care of their animals. At least in the dairy magazines my dad gets, they are constantly stressing animal comfort, prevention of disease, reduce stress, etc. Because this maximizes production. First, those documentaries are biased, and second, those farmers aren't good at their jobs. Our cows seem happy and content, and why shouldnt they be? Plentiful food and water, we keep threats away(which is unfortunately why predators are often endangered or threatened), we do everything we can to make them comfortable, healthy, and happy. Keep in mind cows don't care about being in captivity, they don't have the concept of freedom. They just want food, safety, and mating.
Hope this doesn't sound harsh, but that argument is wrong. A good farm is supposed to be the ideal environment for the animal, the same way a garden is supposed to be the ideal place for a vegetable. The animals die much more humanely than in the wild. I facepalm every time i hear on of those "it is more ethical to hunt than buy from the store" arguments.