Why do they call it root beer?!

Original root beer was alcoholic, and brewed the same way as beer, and as it is made from a root it got the name

Hardly rocket science.

Root beer is a carbonated, sweetened beverage, originally made using the root of a sassafras plant (or the bark of a sassafras tree) as the primary flavor. Root beer, popularized in North America, comes in two forms: alcoholic and soft drink. The historical root beer was analogous to small beer, in that the process provided a drink with a very low alcohol content. Although roots are used as the source of many soft drinks in many countries throughout the world (and even alcoholic beverages/beers), the name root beer is rarely used outside North America, Britain and the Philippines. Most other countries have their own indigenous versions of root-based beverages and small beers but with different names.

http://en.wikipedia.org/wiki/Root_beer

But it was originally brewed the same way many sprits it is just not fermented to create booze.