In this article, the author states that not all animal life survives by taking another animal's life by showing examples of animal pairs where one (or both) obtain something valuable from the other side without killing them. Usually, relationships between these pairs can be in one of the following categories: parasitism (Ex: mosquito and human), commensalism (Ex: whales and barnacles), mutualism (bees and flowers), symbiotic (human and dog).
Therefore, one of the best ways to phrase this would be:
While some living things need to eat other living things to survive, many others live in harmonious relationships with those around them with no need to kill them to survive.