I always wondered why I would find bite sized marks in my bettas elegant long veil tail, but I just caught one of my small neon tetras in the act of nipping his tail
His tail does heal really quickly though because those missing parts seem to fill back in within a day or two and his tail has really come a long way since I bought him at a lfs. All the fish were added together when I set up my 29g tank 2 months ago, don't get me wrong, my betta is the alpha fish between the tetras, guppies and shrimps but those small neon tetras are really quick. It does make me wonder how amazing his tail would look by now if it wasn't being nipped at.
So if you are thinking about adding neon tetras as tank mates to your betta, they are potential fin nippers