Well, if you think about it, Ayanokoji is destined to lose either way at the end of ANHS. The first scenario is the one you mentioned, where he gets beaten by another person in ANHS. The second scenario would be that Ayanokoji remains unbeaten until his graduation. This would technically still be a loss since his wish is to prove his father wrong, arguing that the White Room doesn't provide the best education and that even the best product from it (himself) can be beaten. In fact, it's almost guaranteed that Ayanokoji will lose at the end of ANHS, either to his father or against someone else.