I see you're talking about the various scale-style armor sets. These are tank armors that a LNC can also wear, but doesn't need to wear to do it's job in a party setting. Since anything you're doing to get these "pink" versions requires a party, these sets are designed as a usable upgrade for the tank in your group and as such, they get first pick so they can do their job better. Usually there is one set of gear for each role in a given dungeon.

It's worth noting that anything that is "pink" can be bought on the market boards in it's regular form, and if you get the HQ version, the stats are comparable to the "pink" versions. If you meld materia to it, it's even better.