Seirei Tsukai no Blade Dance - Vol. 1 Ch. 3

[MangaDex]

 

[Kaarme]

So, basically, the headmistress only cares about Kamito likely having much better chances to win the blade dance festival than any of the existing students. Having a dude suddenly attend the all-girls academy, leading to all sorts of trouble easy to imagine, is of no concern.