Alright boys so I think the DEEPEST LORE is pretty obvious now see pic for the cliffnotes version.

-Professor Burnet (from Dream Radar) and Guzma are siblings.

-Kukui married Burnet (and Burnet is wearing his lab coat in Dream Radar, see pic, it's the same coat)

-Guzma's beef with Kukui is thus given another layer of "it's personal" to it because he stole his sister in addition to the "rejected trial captains" thing