Alternatively, the basic reason is that mirrors reverse front and back.
s of left
describe the relation
between "this side"/"that side" and front/back. On the contrary, top
of the front/back direction
. In the mirror image, "this side" and "that side" are unchanged, just like top and bottom, but front and back are swapped, so in effect left and right are reversed.
Interestingly, a combination of two mirrors at a right angle does not reverse left/right. In addition to front/back, it reverses the sides. The net effect is like (-1)*(-1) = 1, and the notions of left/right are unchanged.