Hmm... tough one. I'd say you unfriend him on Facebook, and just play the game. It's not about the person on the other side of the board, it's about the board itself. If he keeps on bothering you, you might have to block him (on both platforms). But whatever you do, don't resign! You're not a coward (I hope)! Best of luck solving this issue :)
Chess fraud: how do I abandon the game?

report them for sandbagging their rating. I think challenges out of the blue are best done unrated. Last time I accepted a rated challenge, they cheated and it took almost 2 weeks for their ban, I thought I'd never get my points back for ages. "Then, he asks me to be his friend on Facebook" This too might be bannable if chess.com finds a suspicious pattern of the opponent doing it to many other people
Several days ago, a player wrote to me asking to play a game. His profile said his rating was 1116, and he seemed friendly enough, so I (at 1193) challenged him. The game is currently on move 2. Then, he asks me to be his friend on Facebook, so I friended him. His first message to me on Facebook Instant Messenger announced that he was actually a highly-rated player (2100), and he would improve my chess for $10/hr. I didn't ask for any lessons or an advertisement. If I resign from the current game, I'll take a hit to my rating. I want to abandon the game. Does anyone know how? And is there possibly another way to handle this? (The game is here: https://www.chess.com/game/daily/514501535