Smug pretty teacher smile.
It's the world of an RPG game, which means it's basically going to be a shounen as a world where all conflicts inevitably lean towards fighting it out as a solution.
With that in mind, Anoi is being way more reasonable than most jobbers with his role in other stories. Rather than gossip behind the MC's back or grumble or scheme with petty tricks, he's just up and saying it.
His argument isn't bad either. Just because the principal is strong doesn't mean she's immune to corruption. If anyone would be able to cheat their way into this position, it would be the ducal family.
That said, they should probably make it clear that Zenon doesn't actually have to win the duel (which he will because he's the main character) to justify his presence here. As long as he has a good enough showing, people should be satisfied.
In fact, it would actually be a better demonstration if it was Zenon vs Yuno. The biggest counterexample to the accusation is Yuno's existence as a commoner and letting them both show their stuff against each other should do the trick no matter who wins.