Yea, I don't know why the writers give characters such contrived things to fight about.
It reminds me of Season 3 where Blaine randomly got on Sam's case about being a stripper.
Seriously, there are better reasons they could give for Hummelberry to fight. They're both ambitious Type A's, it shouldn't be hard for them to get heated competing at NYADA, but the writers are lazy and give them stupid crap to fight over.