Humans actually don't have to cook our food and there are many meat dishes such as sushi and steak tartar, which are served raw. In general, however, food is cooked for health concerns.

For instance there are several types of parasites and pathogenic bacteria that can be transmitted to humans by eating uncooked or poorly cooked meat. By cooking the meat properly, these organisms are killed. For most of us, these infections might make our lives a little unpleasant, but would probably not kill us. However, because such a high concern in modern western society is focused on quality of life, we choose to do whatever is necessary to limit any unnecessary unpleasantness.

As far as other animals are concerned, the risk of contracting a potentially debilitating parasitic infection is a matter of everyday life. These animals don't really have a choice. While some individuals may feel under par as a result, we typically don't notice it. In their weakened state, they may also be more prone to predation and end up becoming someone else's dinner. If you've ever had a sick dog or cat, you notice that they hide their illnesses quite well, and typically a critical health condition is not spotted until it is too late to really do anything about it. In the wild these individuals would be the first ones to be hunted down.