So what was the duke and the emperor beef again?

Emperor is uncle to the duke, the duke should be rightful emperor, emperor feels like his position is always threathen by duke, but ig for public image he cant kill duke

adding on, the emperor also had arzen's dad assassinated. now that arzen's grown up, he looks just like his father, and the duchy is well respected across the empire, so he feels like his position in in jeopardy