I think it comes from a viewpoint that all death is bad and all life is good. something I think is probably pretty culturally specific and kinda ingrained in me since childhood. I was raised Catholic with everyone around me believing that after you die you go to Heaven, but still family members dying was a tragedy, instead of say, it being a celebration since didn't they just get into eternal paradise?
But death isn't bad. It's actually necessary for life to continue. The circle of life, carbon cycle, nitrogen cycle, all that stuff. From that point of view, eating other animals is nothing. It's an efficient, and delicious, way of surviving and passing on genes. We're not above nature. We're in a closed system here that we can't ever rise above. Although with that point of view stuff like climate change takes on a different meaning. If we can't rise above nature then climate change is a natural phenomena even though it's accelerated by humans. Just like the Great Oxidation Event.