@Gotham2298 : I think it's more about reputation.
Considering this is THE head's invitation, not showing up regardless of excuse would be implying that you've got something more important than obeying the head.
As Tatsuya mentioned in this chapter, whether Miyuki show up or not won't really affect her becoming the next head, just at best postpone it (which is something Kuroba also said)
But since the opponent(s ) are so determined to do this, he decide to just crush their plan and make this happen.
Though it wouldn't surprise me if the whole thing is basically a test to see if he can overcome such ridiculous odds that he is considered the strongest guardian that can't be replaced (i.e. to shut all the people saying Tatsuya shouldn't be by Miyuki's side up)
Minami also had a combat session as her graduation test before becoming Miyuki's guardian.