From the other side, when I was a student PPLer, I was told from the outset by my instructor that if there was ever any problem, and I felt I wanted to change instructor, that I should say. They explained that sometimes it is just a personality clash, which I believe is very true, or sometimes one instructor's style suits a student more than another's.
All of the instructors used to say this to their students at the beginning and at the school where I trained, the occasional student would fly with another instructor. And sometimes they would come back to the original instructor.
The attitude was always very open, and with the "get out clause" of "clashing personalities" no-one needs lose face.
I think the CFI of a school should maybe get instructors to do this.
Lets face it, we've all flown with someone who we don't get on with as well as others, sometimes there is a drastic difference. Sometimes a different instructor can put a different perspective on something.
Also, if a student was having a problem with a particular exercise it was common practice to suggest they have a flight with another instructor.
A flying school is not a place for huge egos.