As shown in the figure, two rays A and B are reflected by a mirror...

The incident rays $A$ and $B$ are parallel to each other.

After reflection, the corresponding reflected rays $A'$ and $B'$ are also parallel to each other.

For parallel incident rays to remain parallel after reflection, the normals at the points of incidence must be parallel. This is only possible if the reflecting surface is flat.

In the case of spherical mirrors (concave or convex), the normals at different points are not parallel, so a beam of parallel rays will either converge or diverge after reflection.

Therefore, the mirror must be a plane mirror.