Reviewer is not really very bright, is she...
Call this a shot in the dark but perhaps the reason there are no pet classes is because *EVERY SINGLE CHARACTER* is effectively a pet class. Let's see what a pet class would be like:
* A main character providing the majority of the role be it tank, support, damage, etc - check.
* An AI controlled companion of some sort - check
* ....who can be controlled by a series of mode settings - check
* ....with a range of activatable abilities that can be set on automatic - check
The reason you don't have a "pet class", as you put it, is because trying to manage 2 separate AI controlled characters simultaneously would be a nightmare, in addition to being grossly overpowered in PVP.