Why do we see the writing reversed in the mirror?

Answer 1

because a mirror reverses everything. Try this:
Look in the mirror
Raise your right hand.
In the mirror it seems as thought the reflection's right hand is raised, but if you look closely, its really the left hand being raised. That's just what happens in any relection.

Answer 2

hopefully this will answer your question:

Effects

In a plane mirror, a parallel beam of light changes its direction as a whole, while still remaining parallel; the images formed by a plane mirror are virtual images, of the same size as the original object (see mirror image). There are also concave mirrors, where a parallel beam of light becomes a convergent beam, whose rays intersect in the focus of the mirror. Finally, there are convex mirrors, where a parallel beam becomes divergent, with the rays appearing to diverge from a common intersection "behind" the mirror. Spherical concave and convex mirrors do not focus parallel rays to a single point due to spherical aberration. However, the ideal of focusing to a point is a commonly-used approximation. Parabolic reflectors resolve this, allowing incoming parallel rays (for example, light from a distant star) to be focused to a small spot; almost an ideal point. Parabolic reflectors are not suitable for imaging nearby objects because the light rays are not parallel.

A beam of light reflects off a mirror at an angle of reflection that is equal to its angle of incidence. That is, if the beam of light is shining on a mirror's surface at a 30° angle from vertical, then it reflects from the point of incidence at a 30° angle from vertical in the opposite direction.

Answer 3

I think it's a explanation based on
how the camera works, also. But I don't know the reasons why. Your eyes see things, as a camera one way and the retina and the camera reverses the objects.