A canonical example could be about the "leap year" rules.
For context, the Earth makes a full rotation around the Sun in about 365.2425 days, so we use leap years to compensate:
- add 1 day every 4 years (365 + 1/4 = 365.25)
- but not every 100 years (365.25 - 1/100 = 365.24)
- but add a day anyway every 400 years (365.24 + 1/400 = 365.2425)
Suppose most people only know the first part (1 additional day every 4 years). If we ask "is 2000 a leap year?", they would answer "Of course, 2000 is a multiple of 4". And they would get the correct result.
Now, suppose someone started to study the "subject" (here, there is nothing to study, this is a trivial example for illustration), and is aware of the second rule (but not the third one). He would say "Ahah, no, 2000 is not a leap year, because it is a multiple of 100". But he would get the wrong answer.
My impression is that this kind of mistakes happens often while learning a subject: by studying, we encounter exceptions or surprising facts, that we may apply too broadly (to the point we make absurd claims, but that appear absurd for the wrong reasons).