I am so confused by that GF. Is her ego so fragile she's trying to embarrass the other guy because she wants to assert her BF is that much better in some way (ie. Didn't have to retake a class.) But for whom? She's already trying to push MC towards this guy, what's the point in highlighting whatever faults he has.
I swear, we're probably going to see an arc where she gets dumped cause she'll get caught by her BF trying to seduce the other guy. And she'll probably say something like how she wanted him all along but settled for the other guy cause he's not as good looking.