I think knb's "weirdness" and pjebys "loyalty" seem like good reasons.
Another reason could be that they feel discomfortable about you making another decision because it could imply that they are making wrong life decisions. So persuading you to make the same choice also reassures them that they have have made the right choice for themselves, thus removing a stress source.
Also, a very simple explanation (you kinda mentioned this with the different values) they might just be trying to make the "correct" decision for you. People differ in knowledge. They might just think they make better decisions than you do and try to make your life better.
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Thanks, that explains the 1/2, 1/6, etc. thing. So 1/24 is indeed next.
I still don't get the folding thing (vs. making the picture diagonally symmetrical) very much, but I kind of get it, so I'll leave it be.
Maybe you don't just make the picture diagonally symmetrical because then if you would integrate over all the probabilities you would get 200% (because you represent every situation twice)?