Why wont the 2013 ford f150 supercab rear door open?

The most likely reason that the rear door won't open in Your 1013 Ford F-150 super cab is because the latch lock cable end has broken. The cable ends made of plastic and overtime become brittle and break. This causes the cable to activate the latches. There are aftermarket kits that fit perfectly on the cable and are made of metal, so they won't break so easily. You will have to remove the door trim panel to get to the latches. You're going to need a few hexAnd torx sockets with a ratchet and a Phillips screwdriver. A panel clip trim removal tool would be nice to have to make it easier to pop the clips, but a flat blade screwdriver will work, but You may break more clips. Remove the handle and latch to reconnect the cable.