Actually, that’s not really true. Biologists generally agree that predators, prey, parasites, and competitors can exert natural selection on the other species they encounter, but we’re still not sure how much those interactions matter over millions of years of evolutionary history.
On the one hand, groups of species that are engaged in tight coevolutionary relationships are also very diverse, which could mean that coevolution causes diversity. But it could be that the other way around: diversity could create coevolutionary specificity, if larger groups of closely-related species are forced into narower interactions to avoid competing with each other.
Part of the problem is that it’s hard to study a species evolving over time without interacting with any other species—how can we identify the effect of coevolution if we can’t see what happens in its absence? If only we could force some critters to evolve with and without other critters, and compare the results after many generations …
Oh, wait. That is totally possible. And the results have just been published.