That mindset does not leave much room to interpret killing as anything but hateful and evil. The animal does not want to die any more than you or I would, and thus making it die is deeply wrong.
But for much of human history, killing animals was considered a fundamentally different act from killing a human. (Heck, killing humans was also considered much more acceptable in certain situations.)
If you spend time around hunters or farmers, they have much more complex relationship with animals than most urban dwellers do. The latter tend to have a simplified view that animals are sort like dumb, well-meaning people in animal costumes. The former respect that we have many things in common with animals, but also many differences. Eacn animal has a complex role in our society that has aspects of being material property, a natural resource, and a living thinking being.
In an urban environment, the only killing you are likely to experience is violent acts in movies and violent attacks between humans. Out in nature, you experience a greater range of ways that animals physically interact. And, if you spend time with farmers, you understand what it means to both care for and kill the same animal, to give it both a good life and a good death.
It is obviously not morally wrong for a wolf to eat a chicken. While we humans may "know better" and choose to not do that, we are also quite closely related to wolves. The chicken has a right to live a complete chicken life, and we also have some right to live a complete life as an omnivorous primate with the sharp teeth and stereoscopic vision of a predator.
There is no cognitive dissonance in killing an animal for food as long as you are willing to accept that animals are different from humans in some important ways.