Why would a guy ask me to call, not answer when I do, then get upset when I stop calling?
It's all about control. He wants to have the control. If a guy asks you to call him, it's because he has no intention of calling you and doesn't want to be asked "Why didn't you call?" By putting the ball in your court by asking you to call, you are put in a position of not being able to ask why he didn't call, because he had told you to call. See how sneaky this is? If a guy asks you to call him, he is probably not that interested, otherwise, he would take charge and call!
This is why he doesn't answer when you call. He wants to keep you at the periphery of his life, so that you're there when he needs you, but he doesn't want you to be involved in his everyday life. This explains why he gets upset when you don't call. He wants to know you'll be there for his own selfish reasons, and feels he's loosing his grip on you when you don't do what he says.
My advice: Time to go.