Why do mirrors seem to flip left and right, but not up and down?

A mirror does not swap left for right any more than it swaps up for down. What it reverses is the direction perpendicular to its surface, so front and back are exchanged. The apparent left-right flip arises because we compare our image with ourselves after imagining that we have turned around to face it, and that imagined turn is usually made about a vertical axis. A psychology paper on the topic describes the mirror as optically reversing the axis perpendicular to its surface, and then asks what the perceptual consequences are. [1] [2]

A physics answer by Mark Eichenlaub, which refers to a video of Richard Feynman discussing the question, uses a blue dot and a red dot in front of a mirror. The blue dot on your right is still on the right in the image. What changes is the order along the line running from behind you to the mirror: in reality it runs your back, your front, the dots, the mirror, and in the image it runs mirror, dots, your front, your back. The dot is lined up with your right eye in reality and with the image's left eye, because the image faces you. [2]

Because the body is roughly left-right symmetric, the image looks like a person who has simply turned around. The same answer notes that a person whose two sides look different, such as the fictional Two-Face, would see at once that the image was not an ordinary turned-around version of himself. For him, left and right have not been flipped so much as forward and backward, producing a version that cannot be rotated to fit over the original. Wikipedia likewise says that reflection changes chirality, from a right-handed to a left-handed coordinate system. [2] [3]

The Physics Classroom tutorial points out that the image is upright, not inverted, yet seems reversed left to right. It argues that this is a frame-of-reference effect. Letters on a transparency held up to a mirror look reversed in the image, but they are already reversed from the viewpoint of the person holding the transparency and facing the mirror. Looking in a mirror amounts to viewing yourself from the front, which is a switch of reference frames. [4]

A 1974 Journal of Philosophy paper by Ned Block adds that the sense of reversal depends on how we imagine turning an object to face the mirror. Most people rotate a placard about its vertical axis, which produces a left-right reversed text. Rotating it about its horizontal axis would produce an up-down reversal, and if that turn felt more natural, people might ask why mirrors reverse up and down instead. [5]

The physical facts are not in dispute. What differs is which explanation is offered as the answer. One camp, represented by the front-back account and the Physics Classroom, says the mirror reverses only the perpendicular axis and the rest is a matter of reference frames. The philosopher's paper holds that the question has many interpretations. On some, the right reply is that mirrors do not reverse left and right at all. On others, the explanation lies in the concepts involved: up is defined relative to the earth, so it is the same for you and your image, whereas right depends on the orientation of the person, and you and your image face each other. In that paper's thought experiment, a mirror placed at the centre of the earth would reverse up and down as well. [5]

The psychologists Ittelson, Mowafy and Magid say that an acceptable answer is not found in the literature and treat it as a problem in visual perception. Their experiments found apparent reversals along left-right, front-back, top-bottom and oblique axes, depending on which asymmetries of the object are perceived and on conventional orientations. They concluded that an object appears reversed along the axis of least perceived asymmetry. I found no source here that says which view most specialists hold. [1]