The problem is in the use of language - there is no 'reversal' - it's just a reflection. How about this logical argument:

1. Looking in the mirror with a bag on your right hand, you see an image with a bag on "its left hand". (The image doesn't have a 'left' hand - it's only an image - left and right are your perception.)

2. Have an 'out-of-body' experience - let your virtual self walk around and stand behind the image. Your virtual image has a bag on the hand on the left side of the mirror - "its right hand". The mirror image has a bag on the right side of the mirror - "its left hand".

3. Your virtual self has turned 180 degrees to get to this position, and has therefore undergone a left-right reversal. Therefore, since the bag on the mirror image is on the other hand, it has not undergone a left-right reversal.

Phil