Ambrose is a bully. You've never met a bully?
"The researchers found that children who bullied were often motivated by a desire to increase their popularity and that they chose generally unpopular victims to avoid losing social status... Bullies tend to be aware of the social hierarchy within the class and are seeking the admiration of specific people." [0]
Amrbose (unknowingly) thwarts Kvothes QUEST as part of a petty prank to put him in his place. Kvothe fights back. Once that antagonistic relationship is established, it gets out of hand and there is plenty of motivation to keep it going.
[0] https://www.webmd.com/parenting/news/20100325/what-motivates...
Then, a few episodes in, you meet his parents.
At first.
It's far more than your typical fish-out-of-water setup.
I liked Name of the Wind for the most part but some of the characters were flatter than pancakes. That bad guy student (Ambrose?) has no motivation beyond just being a deliberate antagonist