Fear of losing person X is the first thing that comes to mind. However if person X really would leave you for standing up for yourself than you are not really losing much. Personally I would not do what they requested just to see how they react. The conversation that comes after is what really matters. Do they say "okay" and carry on as if nothing happened? Do they get all defensive and say "You would do it if you loved me"? Do they say "Why won't you do it"?
Base the future of your friendship on how they respond, just be sure to tell them why you are doing so to give them a second chance if needed.