@ShinGetsu It's not her job to keep track of who is or isn't in the student council. She asked last episode "are you in the student council", and he didn't say that he was a probationary member.
She then said "this document is useless" (and since it is needed tomorrow she probably got it delivered late, also as part of the presidents plot to create a stinky scandal.)
He then said "I did that" and while still upset she was then willing to at least acknowledge that it wasn't really/solely his fault.
As for the rest of her issues - president probably picked this particular teacher and method because of their short fuse. So she was a hand-picked bomb for this scandal.