Because the long, flowy fins on many male bettas are a trait selectively bred by humans for looks and showing, they're actually not natural for the species so bettas will often literally turn and bite at their heavy fins. This is especially common with Halfmoons, Doubletails, and even some Veiltails. It can be anything from a couple of nips to the ends of a bettas tail every once in a while, to your betta practically turning himself into a Plakat......and there are numerous possible causes.
In little plain cups where there is so little space, bettas can get easily get frustrated and bored, and also without much room to move often they'll see their colorful tails and just go after them. So its not at all unusual to find a betta with their tails chewed off in pet stores, like your guy, but most of them do perk up and leave their tails alone once they are in a nice proper environment IME. :)