Mirrors don't actually reflect your image from right to left. It's a reflection, not a reversal. Think about it: what's on your left still appears to be on your left. The right-to-left thing is only from the perspective of some other person observing you - that individual sees your left as their right.
The reason for this is that in order for you to see you as this third party would it would be necessary for you to go through the mirror and then turn around. Most people achieve this rotation on the vertical plane, such that the toes of "you #2" would be pointed at the toes of "original you". It's this rotation that makes it appear that left and right are swapped.
If we were able to fly or something and had the option of rotating on the horizontal plane, this would not be the case.