Find a so-called DRM word list (acronym originating from the researchers' names Deese, Roediger and McDermott) and have someone test you: They present you with the word list for a predetermined amount of time during which you attempt to memorize it. Then they ask you to recall which words were present. Along with recalling (some of the) actual words, you are in addition likely to recall a so-called critical word which was not actually present in the list.
A collection of such word lists can be found at https://www3.nd.edu/~memory/OLD/Materials/DRM.pdf
Just because many people makes that mistake doesn't mean that such mistakes are common in everyone.
But even if I didn't, that's not really the kind of thing I would ever call upon my memory for. Usually it is something like (real, recent examples from my life): "Who said what, when, how, and to whom", "who was here and who left first", "did this scene happen before or after this other scene in the movie", "who threw the first punch", etc.
> But even if I didn't, that's not really the kind of thing I would ever call upon my memory for.
But it's the same type of thing! If a DRM list produces false memories, why should these other situations not? You don't even have to reach for the DRM paradigm; it's well documented that witness reports in courts (i.e. exactly the kind of thing you mention) are unreliable.
Its just, many will believe they are rational when they aren't, since their lack of rationality makes them unable to see all the ways they are irrational. But people who notice their own irrationality can just stop doing those things and change their views and therefore becomes much more rational than average.
So we have several layers, we have those who don't see their own irrationality and call themselves rational, we have those who see their own irrationality and call themselves irrational since they are, and then we have the ones who see their own irrationality and takes measures to fix it and therefore call themselves rational. The last group would be the most rational ones, but is still often mistaken for the first group.
Go ask your siblings or parents if you're right.
Memory is a fluid thing.
Could you have a mistaken belief about your memory and it's veracity?
Edit:
> Do you ever sometimes have mistaken beliefs?
I remember the sources of my beliefs. Sometimes I have mistaken beliefs since the sources were wrong or fuzzy, like my parents told me something that I then believed, but then I learned that my parents were wrong. This makes it very easy to correct mistaken beliefs, since you just go back to the sources and verify and re evaluate the information against the new disagreeing information.
Remembering the sources of what you know isn't that much extra information, so it isn't particularly hard to do, but it helps a lot keeping yourself more rational.