Oh god, sensei is the type to say no when she means yes
If it wasn't already clear from how Taiyou easily dragged her into becoming the club advisor.
Seriously though, having to find a replacement should be the school management's problem and not hers. Not being allowed to quit until a replacement is found (what if it takes months, well beyond the usual 30 days notice?) sounds like slavery with extra steps to me. That school is being run like a black company or something? But yeah, it's moot since she ain't quitting soon by that smug look on her face at the end.