Objectively speaking, MC shouldn't have used his demon eyes so easily, exposing his hidden card (worse, it's his trump card!) in front of everyone. Even if the girl got injured, there should have been at least one capable healer in that place. And the blonde teacher will be more likely to get expelled.
Or maybe stupid writing, because why else would a student stood so close to teachers' magic duel?
I mostly disagree.
First, the exposition in an earlier chapter stated that demonic eyes do manifest in humans. Rarely, but with a high cost, so he can pretend that he rarely ever use them because he doesn't want to go blind or mad.
Second, his eyes has several powers. So this is revealing one trump card when he has several. It can even be beneficial as people will likely not suspect the multiple powers. Sometimes, revealing a partial truth helps hiding the whole truth.
Third, this easily builds trust with the girl. His eyes are potentially powerful, but they can also be easy to resist if you have the will to do so. Building trust without using them first will lower her defense.
Fourth, having healers on duty would make sense, but Blondie suddenly used high level magic here, so the girl might not survive this in the first place.
Though I definitely agree that the student being that close to the duel is stupidly bad writing, the MC's action itself isn't inconsistent.