I aggree Alpha, I think it's insane that someone would assume that.
Have you tried a "teachers rate"? Higher rate thoughout the year, but no cost for the summers and march break.
That way you're not loosing any income over the year, it's just squished into a smaller period of time? Just a thought.
I think our rates are justified in the way we present them. If we know we have a teacher we can say to them... here is your daily/weekly rate. I do not charge for summer or march break. If you need care during these times we can arrange a drop in rate at $XX
I wonder if that would work.