It's to do with the class's lore - Carbuncle is stated as a being created from the manipulation of esoteric geometric symbols in an ACN's grimoire, Primal-egis on the other hand, are the essence of a Primal bound to a SMN - Carby hence is not a Primal. This isn't FFXI where Carbuncle was the same as the other avatars you summoned.

Once again, try to look past FFXI and treat FFXIV as a totally different game that does things in different ways.