Portraiture creates the opportunity for a sitter to see themselves as others might see them. Even more so, it creates the opportunity for the artist and sitter to influence the memory if how that person was seen by others, long after it is possible to actually see them in that state (or at all).
Rather than just demonstrating the visual qualities of the sitter, though, it is also an opportunity for the artist to demonstrate their own, unique way of seeing. The reflection of the artist in the mirror is, in reality, an image that is both exclusively available to that artist, and completely unavailable to the artist (without the aid of a mirror). In painting a mirror that contains the reflection of an artist, this image is absurd. It allows the viewer to see the reflection of somebody else as they look into a mirror.