It is caused by front to back inversion. Right and left have meaning only when front is specified. When we look into the mirror, suppose we have left sleeve as green and right sleeve as red. They are indeed on the same side in the image. Is it not? But the image is facing opposite to us so For the mirror person green becomes right and red becomes left. You can understand it this way as well. Write some alphabets on a translucent paper. See this paper in the mirror. The alphabets are laterally inverted. Now see the same paper from the back side, does it not look like the image of the front side in the mirror? Cause is of course the light ray starting from the object is reflected back and hence whatever looks to mirror now looks out of the mirror. That is why I call it front-back inversion.