Here is a paraphrased version of the call:
Me: Hello?
Machine: This is a call from Cardmember Services. We are calling about your credit card account. There is nothing wrong with your account and we are calling to offer an interest rate reduction on your credit card. Press one to speak with an agent.
Me: <presses one>
Agent: Hello? (Sounding impatient)
Me: Hi, I'd like to be removed from your calling list.
Agent: That's not possible.
Me: It's not possible for you to remove me from your calling list? That doesn't make any sense.
Agent: it does make sense. <hangs up>
I have a hard time believing that any reputable company would conduct business this way. Please exercise caution when dealing with them.