I've tried reading a couple guides, but the relationship between armor and proficiency points still confuses me.

For example, my shadow Zolnixi has recommended stats in Int. and Agility. The Lightbringer armor set increases Int. and Agility, but the Reaver set is the one intended for Shadow pets. Why would I use a set that doesn't increase the recommended stats?

reaver gear also increases int and agi, but in different proportions. Reaver has a greater focus on agility than int, while lightbringer has a greater focus on int compared to agility
As such, Shadow favours Reaver because it's a primarily tanking element, so it wants more agility for higher defence and evasion generally speaking.
Reaver also has higher str than dex, while lightbringer has higher dex than str, so Reaver gives a little more of a physical defence boost while lightbringer has a little more accuracy and crit boost.

You can absolutely use lightbringer gear on a shadow pet, though, nothing to stop that happening.

Light healers tend to run Pyromancer more than Lightbringer because people like the dex build for the crit beam and fairy light, and water and earth can trade up tidal lord and warden pretty easily

Ok, that makes sense. So there's a little more to team building than I thought, haha. Thanks for explaining!