There are two reasons to it. First, the relatively dry refrigerator air draws more moisture out of foods than does normal room-temperature air. Second, the bonding between the starch and water molecules is weaker at refrigerator temperature than at room (and freezer) temperature. Consequently, bread will turn stale more quickly in the refrigerator. On the other hand, if the bread is not located in a cool, dry place and is not kept in an airtight bag, it might be attacked by airborne mold spores. If so, mold could develop on the bread's surface at such an accelerated pace that the bread would have been better stored in the refrigerator, despite the staling factor.
For optimal long-term storage, freeze the bread (it freezes well). Wrap the loaf well in plastic or place it in a heavy-duty, zipper-lock freezer bag. Whatever storage medium you choose, be it breadbox, refrigerator, or freezer, minimize moisture loss by keeping the bread well wrapped.