My "alt" only has one class unlocked (the starting class). And it's level 16, so no jobs. No DoH, no DoL. Just CNJ. And she has 8 gear sets. My main has 7 classes, 5 jobs, 8 DoH and 1 DoL for a total of 21, and he has 26 gear sets total.
Perhaps my alt is already getting a gear set for the first DoH and first DoL classes even though I haven't unlocked any yet (i.e. you won't see an increase in your gear sets until the 2nd DoH/DoL you unlock) along with 5 extra slots?