The difference is you, as a human, have a choice. You are capable of living a healthy, full life w/o eating the flesh or excretions of animals. The bear (or lion or tiger) has no such ability to choose.
However, the larger point is that the idea that it is immoral to kill to sustain yourself goes so far against the way nature is organized that I find it ridiculous. While it's true that morality often means going against natural tendencies, in this particular case I find it exceedingly opposed to the regular order.
So, I personally reject the very premise that it is in any way immoral to end the life of anything except members of your own species, as long as you don't do it out of cruelty or greed, and as long as you do not eradicate the entire species through your actions.
This is an appeal to nature.
> ... as long as you don't do it out of... greed
How does "I like the taste of cows and milk" not meet your definition of greed?
A moral system that would consider the vast majority of natural life to be immoral is dubious to me. It's not simply an appeal to nature, it is a particular choice for the way I think a moral system should be evaluated.
> How does "I like the taste of cows and milk" not meet your definition of greed?
Greed always refers to excessive consumption. If you go on an all-beef-and-milk diet, and slaughter hundreds of animals a year just to feed yourself, you are probably being greedy. But eating well-raised beef, in quantities that do not encourage others to find the most efficient ways of raising as many cows as possible in as little space, doesn't fall under my idea of greed.
A single dairy cow, if well raised, can give enough milk for a family of 2 or 3. With two cows, one can have a constant supply of milk by essentially having each cow produce a calve each year. The calves can be raised for a while and then sold on to a bigger herd or slaughtered for food. When the animal is slaughtered, as much of its entire body should be used, not just a few of its muscles. The cows would be kept well fed, warm over the winter, clean and free of diseases. In the warm months, every day they would be taken out to pasture and returned home.
Of course, this means that cow meat would be something that people should expect to eat a few times a year, not daily or weekly. The same would apply to most or all other farm animals. Overall, adding some extra efficiency from larger herds as well, meat could probably be consumed something like once a month, while still raising animals in good conditions. Milk and eggs can be consumed almost daily without forcing others to keep animals in inhumane conditions.