Before I answer your question, I'll ask you one: why are you friends with your ex on Facebook? What are you hoping to get from it? Is it really about friendship, or do either -- or both -- of you hope for something more? That's the real issue here.
Whether or not his request is reasonable depends on your motives. If you dated your ex from age 5 to 20 and still care for him and want to keep in touch in a platonic way, there's nothing wrong with that and your boyfriend is being a dink. But if there's more to it, then obviously you have a problem. You really need to think about your motives and be honest with yourself. You might also ask yourself how you'd feel if the tables were turned and he was keeping up with old girlfriends and didn't want to drop them even though it troubled you.
Really, though, does it even matter if his request is reasonable or not? Isn't love sometimes about sacrifice, or doing something our partner wants us to do, even if it's unreasonable, simply because they want us to do it? I think it is. If these sorts of demands from him are par for the course, that's a problem, and I agree that you should stand your ground. But if not, why not do what he wants this time? Why not choose him over your ex? Or over your own pride or stubbornness?
Yes, his methods are absolutely deplorable -- threats are lame, ultimatums ineffective. It's not a good sign for the future of your relationship, frankly, and something you need to discuss. But the old saw about choosing your battles comes to mind, and keeping an ex as a Facebook friend doesn't seem to me like one worth fighting.
I could be wrong, though. There's a first for everything.