According to this paper, vegetarian philosophers argue that livestock live lives not worth living because of the cruel treatment they receive. The paper then argues that wild animals receive worse treatment from nature. Therefore, their lives are similarly not worth living. Reducing suffering is the goal, and not living is better than living, so reducing the number of wild animals is best.
There are a number of good arguments to this. One would be that humans breeding livestock increases the amount of suffering, whereas wild animals are not bred. Another is about directly benefiting (eating) from this suffering verses not benefiting. Yet another is that active harm from cruel treatment is different from passive harm by "not helping" the wild animals.