(By coincidence, my previous post made reference to a proof that all triangles were isosceles and I was thinking of the very one Andre posted... Of course, I did recently read the book "Mathematical Circles" [I enjoyed it greatly!] and saw the proof there, typos and all.)
> I want to continue that proofs of wrong statements are just > one kind of useful ways to puzzle children. [...] > But all this is just a preparation. What should > come next is training in solving problems right - that is so > that to avoid all these `miracles'. That is why it is so > important for children to solve problems where it is clear how > to check the answer and to find out whether it is right or wrong.
I find nothing to disagree with here. "Proofs of wrong statements" are certainly not the main course! They are an anjoyable and useful supplement, though, and particularly relevant to this thread of "plausibility arguments".