Paper reflects all the lights of the spectrum so it looks white. But mirror also does that then why is not white?
There are multiple factors to why this happens. I shall start with the simplest one first.
The surface of the paper is evidently rougher than the mirror surface. This contributes to diffuse reflection on the piece of paper. Hence, light from different parts of the potential image(the image that would be reflected on a mirror) will reflect at different angles. The diffuse reflection will scatter the reflected light rays, hence there is barely any image seen.
Secondly, the more advanced reason.
Particle physics: Light penetration, specular and diffuse reflection
Due to the smoothness of the glass surface, more specular reflection occurs as opposed to diffuse reflection. Specular reflection is when the photons come into contact with the silver particles of the mirror, and when these particles achieve excitation state to release the photons. However, when the photons are released into the material(occurs more in paper than in mirror), diffuse reflection occurs.
In specular reflection, the angle of incidence and the angle of reflection will be exactly the same, so your eyes, nose, ears, etc. will appear at the same position. Diffuse reflection, which happens in paper, causes the light rays to reflect off at different angles, thus forming a poor image. This is due to the largely inactive particles of the paper, which cannot easily be excited by photons.