Mirrors flip the front-back direction, not left-right or up-down.

When you stand in front of a mirror, the image you see is reversed along the direction perpendicular to the mirror surface — that is, front and back are swapped. Everything on your left side stays on the left side, and everything on your right stays on the right side in the reflection. The mirror does not perform any left-right or up-down reversal on its own. This flipping in the front-back dimension is the only reversal that occurs because the reflection happens across the mirror's flat surface.