why it is inscribed on rear-view mirrors that"THE OBJECTS ON THIS MIRROR ARE CLOSER THAN THEY APPEAR

The curved mirror image reveals a smaller angle, and therefore it appears to be further away.  Notice that this is in spite of the fact that the image is actually closer to the observer than it is for a plane mirror.  The fact is, the apparent distances and sizes of objects (or images) are gauged by the angular size and by their sizes relative to each other, not by their actual distances and sizes.

You can see the image seen by the eye or obsever is samll therefore it appers that it is farther away.