Did you remember that one goes clockwise and the other counterclockwise? It could be that you (or someone else before you) were trying to loosen it, but were actually tightening it more and more, until it froze.
You might put some WD-40 on it, let it sit a few days, put it in the freezer for a few hours so the metal contracts slightly), take it out, heat the lock-nut slightly with a with a torch (so the nut expands), lay the nut straight on an anvil, put a ball-peen hammer on top and whack it hard with a sledge straight perpendicular on the nut (so shock will unfreeze the pressure where metal is jammed against metal), put it in a big bench vice, lock it down well, put the longest open end wrench you have on it-do NOT use a crescent as the jaws just don't stay tight and will round-over the vertices [corners] of the hex nut), slip a longer steel or iron pipe over the handle to get more torque, then have at it. Once loosened, the lithium grease mentioned above will be a good preventative to a repeat.
The reason one goes clockwise and the other counter, is so you can tighten and loosen it with both ends stationary, like a turnbuckle. If a 3ph implement is already attached, you can shorten and lengthen the link without disconnecting it. You loosen the lock-nut, adjust, then retighten the lock-nut, all w/o disconnecting the ends. The reason that rectangular loop is on the side is so you can slip in a big screwdriver, chisel end tire tool, pipe, etc. under it as a lever and get some torque to turn the thing in this manner.
