The real answer to this question is a simple matter of light reflection. Rays from a light source bounce off various parts of your body, then they reflect off the mirror and into your eyes. Unless there's a black hole nearby, light tends to travel in a straight line. Albert Einstein's Theory of Relativity or other smartasses may wish to dispute that, but I'm a Newtonian at heart. I like to keep things simple.

In order for a mirror to flip the image one hundred and eighty degrees to your brain, it would have to be reflected at least twice. In other words you'd need two mirrors. Or the mirror would have to be specially constructed to cause the light rays reflecting image to your eyes to be reflected on the diagonal as well as the vertical and horizontal. This is possible. It's one of the fun tricks you'll find at carnival fun houses.

Standard run of the mill mirrors though just reflect what's there. The light bounces off your left cheek, hits the mirror direct and straight on, then bounces into your left eye, and you see your left cheek where it'd be your right cheek if that other you was your twin and not just a reflection. Confused? Good. Now, run along and find a zebra crossing.