Disclaimer: I'm not a physicist and I don't claim to be one so if I have any mistakes I’ll be glad to be corrected.
One feature of the standard model of particle physics is that the weak force is not symmetric with respect to a parity transformation (to be more specific only left handed fermions interact with the weak force).
This is an example of a special kind of counter-intuitive result that defies a symmetry that looks extremely reasonable given our intuition about the world. This implies that the world we see when we glance at the mirror is "unphysical" (or at least obeys a different law for weak interaction).
I'm looking for results in maths where an obvious symmetry was suggested by a certain problem yet careful consideration revealed that the symmetry is in fact broken for certain cases.
Although there are many threads in SE about counter-intuitive results in maths I don't think my question is a duplicate. If it is indeed a duplicate or not at all appropriate I'm sorry.