"Ask to speak to a supervisor / manager" is what Americans do. It's part of the culture, in the same way tipping is expected, regardless of the level of service. So the agent doesn't really take it personally when you essentially call them incompetent and ask to speak to somebody higher up.

Iberia call centres don't have "supervisors" who take calls. Getting all shouty and asking to speak to a manager will get you nowhere. All you can do is hang up politely and call back awhile later (if you call right back you might get the same agent)

Besides that, cancellations are done by the back office. No matter what a call centre agent says, the back office will do things properly. Slowly, according to the queue. So calling back 10 times to try to move things along - essentially by being annoying so that somebody solves your problem - is also counter-productive because the people on the phone cannot actually expedite anything.

If you can understand and live with European cultural norms, then Iberia Club is perfectly fine. If you want an American-style customer service, you need to find another loyalty programme...