They have functional claws on the first and second digits of their wings. Before they can fly, they can use these claws to climb through the branches to avoid predators. For the continuation of the hoatzin species, this is a very good thing, because they can't fly at all until they are 60 to 70 days old. Even the adult birds are poor fliers. That's an extremely rare diet for flying creatures.
Leaves are a comparatively low-energy food source, and flying demands a lot of energy.
Recently, a team of U.S., Venezuelan, and British scientists, led by Alejandro Grajal of the University of Florida, took a long careful look at hoatzin feeding habits, anatomy, and digestion. They found that the birds selected mainly new growth from relatively few kinds of plants. The birds have a unique digestive system anatomy. That is why hoatzins fly poorly. The interior workings of that strange digestive system are what make hoatzins the virtual equivalent of flying cows.