The thesis of John Green that 'the greatest evolutionary advantage an animal species can have is being useful to humans'. A clear agreement or disagreement on this statement without a look at the facts first will not be correct.
On one hand, animals like dog, cat, cows, and goats have become domesticated over time. The ability of these animals to provide something useful to the humans have made them to adapt domestication. And the domestication have certainly helped them to increase their numbers and pass on their genes, which is the basis of the evolution and natural selection. In the cases of these animals, their usefulness to the humans have worked out in their favor and ensured their survival.
On the other hand, the animals, such as pig, fishes, and others which satiates the taste buds of the humans are facing slaughtering just because they are useful to the humans as foods. Still, however, their usefulness have made their species to be cared for in well bred farms, which ensures the continuity of their genes in the world.
Hence, based on the above facts, it can be said that the usefulness of animals to humans is the best evolutionary advantage they can have.