Question

Why convex mirror can't be used instead of concave mirror as a shaving mirror?

Answer 1

While shaving our aim is to see enlarged image of our face.

When face is placed near the concave mirror, it produces a magnified image. This enlarged image of face is helpful to do shaving as even small hairs of skin are clearly visible.

In convex mirrors image formed is smaller than actual object thus it can not be used for shaving.