The equations are symmetric with respect to "image position" and "object position": If we start with an object at position $X_o$ and the mirror creates an image at position $X_i$, the swapped positions $X_o \leftrightarrow X_i$ fulfills the equation as well.
Now, if we start with an image at $X_i = \infty$, the light rays, which fall onto the mirror, will be parallel. The mirror reflects these and forms an image at the focal point $X_i = f$.
What happens, if we put the object at the focal point, $X_o = f$? Well, due to the symmetry, the image positions becomes the old object position, $X_i \rightarrow X_o$.
So, also the image is never really formed, we still say that "the image is formed at infinity" just to maintain the symmetry of the problem. However, since this can never be measured, the wording is only a convention, not an experimental fact.