Could you post the answers to these questions please: http://www.bettafish.com/showthread.php?t=49233
My theory is that either the platies stressed out the betta, which prompted him to bite his own tail, or that the platies, being a semi-aggressive fish themselves, started the gang up on the betta and nip his flowing fins.
Personally, I am not a fan of keeping bettas and platies together since platies prefer hard water with some salinity, and bettas are a soft water fish that comes from water with little to no salt content. The color of the platies can illicit aggression from the betta, and the platies themselves can bully a betta. Not my favorite combination. Some bettas just don't have the right personality for a social situation and are only happy when alone.