PUG/MNK/LNC/DRG/GLA/PLD/MRD/WAR/ROG/NIN/ARC/BRD are all Disciples of War. If it is a Disciple of War piece and you are a Disciple of War, you can equip it so long as you are of proper level. Just because its in your inventory does not necessarily mean you are of proper level to use it. If there is anything holding you back (when you look at the item) it will be in red text.

Take a look at the items you cannot equip. See if there is anything in red text.