Why?
Although Adriaen van der Donk could ascribe all sorts of magic properties to beaver products, when he described New Netherland in 1655, by the time the Mountain Men were rambling about the western US it was the beaver pelts that were valuable, for felt. Felting is the process of making a cloth essentially by rubbing and beating fibers together until they tangle into mat. Beaver fur was found to felt extremely well- the hairs are naturally hooked, and a thin felt of beaver hair could still be pretty strong. That thin-yet-strong felt was of great use in making hats, and hats were a required part of almost everyone's costume . "Beaver" became a synonym for hat ( there was a popular tune in the north of England in the later 17th c. titled "Johnny Cock Up Thy Beaver") . Beavers also of course could not be raised in captivity, like sheep or goats- the only option was to search out their ponds in the wilderness and trap them.