DMcG has the explanation right. It is a combination of language and interpretation by the brain. The image of your left side is on the left in the mirror, so where's the reversal? If you imagine yourself standing behind the image and looking out, having turned through 180 degrees, the bag on your (real) left hand would be on the opposite side to the bag on the (image) left hand. It's your brain that's created the 'reversal' when you look at the mirror from the front.

This mental reversal is extremely powerful. BillD mentions the additional inverting lenses in telescopes and binoculars. These were not used in surveying instruments (theodolites and levels), and you soon get used to working with an inverted, reversed image.

Phil