Translation: "You are right but my ego is too precious to accept it."
Ever been accused of being closed minded? I have. Many times. So have you, probably. And here's another thing; I bet that you were called it because you dared to call someone out on whatever flavour of woo or obvious stupidity they were revealing themselves to believe in.
Some Person: "Ahh, so you're a brother Gemini, are you?"
Me: "You do realise that that's all abject woo don't you, and that the movements of objects several astronomical units away in space can have no more effect on our personalities than I can lick my balls, right?"
Some Person: "You know something? Your problem is you're too closed minded."
I was then dragged away by a third party because "Hazelnut, I know you're a rationalist, but there's some very devout people here."
Notwithstanding the fact that astrology is abject woo, and that that the movements of objects several astronomical units away in space can have no more effect on our personalities than I can lick my balls, and that it completely fails to account for what happens in the 34th century and they're called upon to discern the star sign of a person born in orbit about Sirius or Alioth or Chi Herculis, I did get to have a wee bit of fun with this person when I then tried to have them guess my star sign. They guessed Capricorn ("because they're really argumentative") and, of course, were wrong because my birthday is September 11.
As I wandered off to find more beer, I wondered to myself, probably out loud. Why do people persist in believing stuff that is demonstrably false (astrology, homeopathy, psychic powers, freeman on the land, raw foodism, Holocaust denial, God, etc.) but as soon as they're questioned they immediately try to shut down the questioner with an accusation of closed mindedness? It's almost as if they feel oppressed by the very existence of questioning, because the next move is usually to claim intolerance or even racism (e.g. the Ugandan government when criticised over the "kill the gays" bill in 2009 lashed out with accusations of colonialism and imperialism.) This is, of course, when they don't simply rely on the whole "anyone who disagree is a paid shill for THEM," where THEM can be Big Pharma, Monsanto, the government, the vast right wing conspiracy, the lizards, or whoever. Then it hit me. It's just faulty thinking:
Major premise: Science doesn't know everything.
Minor premise: I cannot explain in scientific terms this.
Synthesis: Therefore, it is possible that magic beans cure cancer.
Often this is teamed with an appeal to personal lived experiences. Otherwise known as confirmation bias, of course, because everyone knows that the plural of anecdote is data.
I also get the impression that the "you're so closed minded" line is used as an ego defence system as well. By claiming that skeptics, people who doubt you, etc. are all closed minded, you get to convince yourself and onlookers that you are open minded and open to new experiences and not like those stuffy stick in the muds. They persecuted Galileo, you know! Therefore who's to say that bottom-probing aliens aren't amongst us and real?
Normally I respond to this with a classic line from Dawn of War. "An open mind is like a fortress with its gates unbarred and unguarded." Because when people are willing to open their mind to any old nonsense, they do just that. This is why Freeman on the Land stuff is peddled across the internets. This is why preventable diseases are recurring thanks to the anti-vaccination movement. This is why the Miracle Mineral Solution exists. All of this is made possible by open mindedness and a concept that critically thinking about things is somehow closed minded and therefore bad.
Oh. And one other thing. Being devout in a belief does not mean your belief is immune to criticism or should be immune to criticism.