Every loadout technically has two.. co op and competitive. Check to make sure the items aren't in your PVP loadout.
That could be what is catching some people out - when you hit certain EGO levels and unlock new loadout slots it seems to copy your previous highest numbered loadout (so if you previously had 3 loadouts and earned a 4th, the 4th would be a copy of your 3rd at the time you levelled up).
6 different loadouts might be a bit excessive but there are certainly times when having more than one can be useful.
I have one setup as a sniper / LMG combo that is setup with skills to focus on stealth and taking enemies down with crits from long distance. I have another setup with AR / shotgun which I use primarily for arkfalls and more short range encounters - swapping out some perks for better shield regen on bonus on crit kills, rather than height and range advantage perks. Currently my 3rd loadout is for playing around with alternative weapons - trialling the BMG, Infector and some explosives.
Multiple loadouts is very handy for long battles like arkfalls - if you have 2 loadouts using 4 different weapon (ammo) types it gives you a second set of weapons to swap to if you run out of ammo on your primary choice and don't want to leave battle to look for an ammo crate.
Bump anybody know how to remove items, there no option to