It's a matter of people imputing notions of "special" where they don't belong. Hence the importance of "proof" in math.
ETA: People are surprised that they can turn a sweater inside-out thru a sleeve or neck hole ONLY because they've imputed a "special" ability to the largest hole in the garment. The mathematical concept of "proof" strips away such imputations, leaving surprisingly unsurprising results - in this case, you can reverse a garment by pulling it thru one of its holes, be it the largest, smallest, or even a tear, because they're all just holes with nothing inherently topologically special about them. In a larger social concept: people tend to impute special attributes to various things where such attribution is not warranted; people who understand the concept of mathematical proof are less likely to get caught up in such incorrect imputation.
Ctdonath was claiming that many people notice that a shirt can be turned inside-out through the main hole at the bottom, or a glove through the wrist hole. Far fewer people try turning a shirt inside-out through a sleeve or neck hole, or a pair of pants through a rip in the knee. They then abstract the wrong way from this experience, inventing the idea that the size of the hole is important (or maybe just that the “main” hole is special).
I’m not sure how prevalent these misconceptions are. It would be interesting to do surveys of the general public to see what kinds of mental models people have here.
If you actually tried to turn a pair of pants inside out through a rip in the knee, the rip might get bigger. In fact, it almost certainly would. Likewise for turning a sweater inside-out through the neck hole, it would stretch it out a bit. Yes, it's mathematically possible but there are real reasons people don't treat their clothes that way even if they know they can.
ETA: People are surprised that they can turn a sweater inside-out thru a sleeve or neck hole ONLY because they've imputed a "special" ability to the largest hole in the garment. The mathematical concept of "proof" strips away such imputations, leaving surprisingly unsurprising results - in this case, you can reverse a garment by pulling it thru one of its holes, be it the largest, smallest, or even a tear, because they're all just holes with nothing inherently topologically special about them. In a larger social concept: people tend to impute special attributes to various things where such attribution is not warranted; people who understand the concept of mathematical proof are less likely to get caught up in such incorrect imputation.