One of my pet peeves (and there are many) are people who accuse others of not being open-minded because they refuse to consider a ridiculous hypothesis. Open-mindedness is not the willingness to consider a wild hypothesis. It is specifically defined as examining all of the available evidence with no emotional attachment to the conclusion it points to. Open-mindedness is the willingness to accept whatever conclusion best fits all of the data.
Here are a few examples of the term open-mindedness being abused.
Person A: Aliens convinced President Bush to orchestrate 9/11.
Person B: That's ridiculous.
Person A: Dude, you are not open-minded.
Person A: I think the world is 6,000 years old and God created it in 6, 24 hour days.
Person B: There is a lot of evidence that disagrees with your conclusion.
Person A: You need to be more open-minded.
Person A: All of the Qu'ran is 100% true, inerrant word of God.
Person B: Muhammed did not go to the moon on top of a flying horse and cut it in half with a sword.
Person A: You, my friend, are not open-minded.
In all of these examples, Person A completely misunderstands what qualifies as open-mindedness in a vulgar display of irony, that they themselves are actually the ones who are not open-minded. Again, it means having no emotional conclusion in mind when beginning to inspect the evidence in order to form a belief. Furthermore, it means once a belief is formed, having no emotional attachment to the conclusion when new information is presented that might necessitate changing said belief.
Often times people approach the process of forming beliefs backwards. They begin with a conclusion and accept evidence that supports their conclusion and reject evidence that conflicts with it. This is how wild ideas like holocaust denial, Illuminati, anti-vaccination, Young Earth creationism, etc. thrive. Humans are deeply emotionally attached to their beliefs, so much so that it often begins to become inseparable from people's identities when it is so far rooted in their psyche. This is exactly why brainwashing is effective. People would rather cling, sometimes violently, to an irrational belief than to change it.
People who begin with a silly conclusion in mind like "9/11 was an inside job" have to ignore a lot of facts in order to maintain that kind of belief. They frequently dismiss conflicting evidence to their beliefs with things like "that's the liberal media just spinning propaganda." A reasonable belief, like a good scientific theory, must account for all facts and evidence and more importantly be willing to change when new evidence is introduced.
Here is an example of the correct approach to open-mindedness.
Person A: I think aliens constructed the pyramids to be beacons for their spaceships.
Person B: I have a PhD in Egyptology. We have extensive writings from Egyptian history outlining how the pyramids were built, which Pharaohs built which structure and why. We know the pyramids were used as tombs for the deceased Pharaohs to honor their greatness. That was their purpose. The pyramids are certainly marvels of engineering, although we don't have a full understanding of exactly what methods were used in construction, we can say in no uncertain terms that spaceships were probably not involved.
Person A: Oh, I did not know any of that, and the documentary I watched on ancient aliens didn't mention any of those things. I suppose I was mistaken.
The world could use a lot more open-mindedness and a lot less of what people think open-mindedness is.