Mrerik's answer is correct, but I'd like to add just a bit more.
By the 1850s, the time when Melville pens his tale of passive-resistance, people were increasingly moved out of their lives in the country and into the stifling offices and manufacturing industries that became the norm as a result of the American Industrial Revolution (typically dated as occuring between 1780 and 1860). Many people could identify with Bartleby, who would "prefer not to." Trapped in offices, in unfulfilling work (both mentally and physically), Bartleby voiced what lots of folks were feeling (and continue to feel.) Bartleby is a hero for everyone who would like to tell their boss to take a hike.
(P.S. I named my cat Bartleby. If ever a creature would prefer not to do what you ask, it is a cat! :)
Simply because Bartleby is the perfect antagonist. The very definition of antagonist (one who opposes...) fits Barteby to a tee.
I suppose we could also argue that the lawyer is the protagonist because the story is told from his point of view, and we are privy to all of his thoughts about Bartleby, but I prefer to view it in the opposite direction. Although Bartleby isn't physically or violently causing any opposition, he's a wonderfully written character of opposition. He probalby would have been a joy to witness at a civil rights sit-in!