Mirrors appear to reverse things from left to right because of our perceptions. Our bodies are roughly symmetrical, so the reflection of your left hand looks just like your right hand. For this reason, we tend to assume that mirrors reverse left and right.
But if you hold up an asymmetric object in front of a mirror, for example a saucepan, left and right are not reversed. The right-hand side of the saucepan (for instance the handle) is still on the right, and the left-hand side is reflected on the left. Instead, a mirror inverts front and back.