Stand in front of the mirror and raise your right hand. In your imagination, trace the rays of light bouncing off of your hand, bouncing off the mirror, and entering your eyes. Your right hand is in front of the right half of the mirror (as you look at it) not the left half.

Your head, however, is on the top half of the mirror as you look at it, and your torso is on the lower part. The light is simply bouncing off the mirror at angles that align left, right, top and bottom relative to you.

The image of the human in the mirror appears to be raising the left hand, because your mind has re-oriented that person to assign “left” to that hand. But it’s really just the image of the right hand coming relatively straight back at you. It appears to be the person’s “left” hand because we think of the image as a person facing towards us. But it’s not a person. It’s just an image of you.

If it helps, move your right hand towards the mirror until it “touches the other guy’s left hand” and then back it off. Do this a few times and it should click what’s going on.

All of this assumes you are standing right side up. :0)