Yamada was reasonably certain that Hayami couldn't see him smirk. So Hayami would take a promise of obeisance by force? It was not unlike what Yamada was doing, if Hayami thought Yamada thought he'd appreciate it. The key difference being that Yamada wasn't delusional enough to think that his subjects would be loyal to him, not matter how often he framed it as if they should. Yamada was well aware that fear was what he controlled the school with.

In addendum. Hayami must not realize that even kings could lie. Unless Hayami felt like staying here to oversee Yamada, Hayami couldn't control him. Even the false obeisance amounted to nothing if Aries could bring Libra to his knees. Which he could. They were only in this situation because Yamada had made the foolish mistake of allowing Hayami to manipulate him. Another such instance would never happen again.

"So you say. Are you finished with your speech, principal?"