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White is a perceptual term. See “The Colors of Things” (Scientific American September 1986). In the article, it is shown that vision uses whatever ambient light spectrum as “white” and variations from that as color. White is not a property of paper. More on that later.
Mirrors do not appear white because every line of sight to a mirror maps to a line of sight from the mirror to the scene it reflects without intersecting any other line of sight. The spectral components of the point in the scene is preserved along the reflected line of sight. In other words, in an unchanging scene, the average color reported for a given point of view, distance, and visual angle is invariant.
Paper appears white because, at least for the average human trichromat, the average ambient illumination is a better approximation to what is reflected than that from a single line of sight.
A white pixel on a TV is not white at all, but three physically separated nearly-monochromatic subpixel sources. However, from a distance, RGB components in equal proportion are accepted as white for display purposes.
To demonstrate what you perceive as white, try this experiment. Buy an LED grow light for plants. Direct it at a plant in a room lit by what you think is ordinary white light (incandescent, fluorescent, sunlight, whatever). The grow light has an odd purplish hue. The shadow of the plant on the wall is green. This is because, from the point of view of your eye, the ambient light is a combination of ordinary room light and purplish which your eye perceives as white. The shadow is missing the purplish component. Your eye sees the “white” combination around a shadow missing purplish. White - Purple = Green. This is known as subtractive color by some. The Scientific American article does a better job of explaining this.
So a “white” piece of paper is not white. It reflects ambient light from all directions in equal proportions for all wavelengths and you perceive ambient light as white.
Hope my answer helps!