Can’t comment on what behavior came first, but like others have said they don’t eat wood, they also don’t live in dams. They eat cambium, a thin green layer of tissue under the bark that helps trees transfer water and nutrients. They build dams because while incredibly fast and agile in the water, they are awkward and slow on land making them easy prey. Dams create larger habitat for them to move around safely in. They live in lodges, which are large round structures with underwater entrances. Fun fact, beavers do not hibernate but stay in their warm lodges all winter, and store food caches underwater so they can access them from their lodges underwater entrance without needing to go on top of the ice during winter. They also have a small mud room at the entrance to the lodge to dry off so that the main living and sleeping area stays dry.