Well, I have one.
Why do mirrors reverse seem to reverse left and right, but not up and down? It's... quite easy to see the answer, but quite hard to explain it coherently.
The answer is: because they do neither and we're a laterally symmetrical species.
What a mirror does, is preserve left/right and up/down, while reversing front/back. This is all it really "does". Now, if we ask our brains to take the resulting picture and rearrange it, by imagining that we stand facing in the same direction that the reflection does(restoring the front/back direction), we can do it either by turning our imaginary selves left-right, or up-down. We preffer left/right, because we're laterally symmetrical, so that the resulting rearranged image still makes sense to our brain - it still has one hand on each side, and still stands with it's feet on the ground etc.
If we were a race of sentient chinaware dishes, we would have no such prefference, as we would be both left/right and up/down symmetrical. Then we would be saying that a mirror can do either, but never both at once.
Mathematically speaking, the mirror changes the handedness(I just hope that I'm translating these terms properly) of the reflection's refference system, so e.g. the typical left-handed* cartesian system becomes right-handed.
Other than that, it's all our brains' doing.